Task 3: Evaluate Techniques for Wifi Locationing

This notebook contains the answers to Task 3: Evaluate Techniques for Wifi Locationing.

library(RMySQL)

library(caret)


library(klaR)
#Avoid loading the MASS package after dplyr
#It may cause a mess with the select function

library(dplyr)
library(tidyverse)
library(readxl)
library(knitr)
library(ggplot2)
library(ggfortify)

library(forecast)

library(lubridate)
library(plyr)
library(plotly)


library(gbm)
library(Rcpp)

Retrieve data

The UJIIndoorLoc database (http://archive.ics.uci.edu/ml/datasets/UJIIndoorLoc) covers three buildings of Universitat Jaume I with 4 or more floors and almost 110.000m2. It can be used for classification, e.g. actual building and floor identification, or regression, e.g. actual longitude and latitude estimation.

The database consists of 19937 training/reference records (trainingData.csv file) and 1111 validation/test records (validationData.csv file). The 529 attributes contain the WiFi fingerprint, the coordinates where it was taken, and other useful information. Each WiFi fingerprint can be characterized by the detected Wireless Access Points (WAPs) and the corresponding Received Signal Strength Intensity (RSSI). The intensity values are represented as negative integer values ranging -104dBm (extremely poor signal) to 0dbM. The positive value 100 is used to denote when a WAP was not detected. During the database creation, 520 different WAPs were detected. Thus, the WiFi fingerprint is composed by 520 intensity values.

Then the coordinates (latitude, longitude, floor) and Building ID are provided as the attributes to be predicted. The particular space (offices, labs, etc.) and the relative position (inside/outside the space) where the capture was taken have been recorded. Outside means that the capture was taken in front of the door of the space. Information about who (user), how (android device & version) and when (timestamp) WiFi capture was taken is also recorded.

The datasets contain the following columns: Attribute 001 (WAP001): Intensity value for WAP001. Negative integer values from -104 to 0 and +100. Positive value 100 used if WAP001 was not detected. …. Attribute 520 (WAP520): Intensity value for WAP520. Negative integer values from -104 to 0 and +100. Positive Vvalue 100 used if WAP520 was not detected. Attribute 521 (Longitude): Longitude. Negative real values from -7695.9387549299299000 to -7299.786516730871000 Attribute 522 (Latitude): Latitude. Positive real values from 4864745.7450159714 to 4865017.3646842018. Attribute 523 (Floor): Altitude in floors inside the building. Integer values from 0 to 4. Attribute 524 (BuildingID): ID to identify the building. Measures were taken in three different buildings. Categorical integer values from 0 to 2. Attribute 525 (SpaceID): Internal ID number to identify the Space (office, corridor, classroom) where the capture was taken. Categorical integer values. Attribute 526 (RelativePosition): Relative position with respect to the Space (1 - Inside, 2 - Outside in Front of the door). Categorical integer values. Attribute 527 (UserID): User identifier (see database website above). Categorical integer values. Attribute 528 (PhoneID): Android device identifier (see database website above). Categorical integer values. Attribute 529 (Timestamp): UNIX Time when the capture was taken. Integer value.

Retrieve data from memory:

df_train<-read.csv('./UJIndoorLoc/trainingData.csv')
df_train

df_validation<-read.csv('./UJIndoorLoc/validationData.csv')
df_validation

length(names(df_train %>% select(starts_with("WAP"))))

[1] 520

names(df_train %>% select(!starts_with("WAP")))

[1] "LONGITUDE"        "LATITUDE"         "FLOOR"            "BUILDINGID"       "SPACEID"          "RELATIVEPOSITION"
[7] "USERID"           "PHONEID"          "TIMESTAMP"       

length(names(df_validation %>% select(starts_with("WAP"))))

[1] 520

names(df_validation %>% select(!starts_with("WAP")))

[1] "LONGITUDE"        "LATITUDE"         "FLOOR"            "BUILDINGID"       "SPACEID"          "RELATIVEPOSITION"
[7] "USERID"           "PHONEID"          "TIMESTAMP"       

The dataset contains the expected columns.

Initial Preprocessing

table(sapply(df_train, class))

integer numeric 
    527       2 

table(sapply(df_validation, class))

integer numeric 
    527       2 

All columns are originally integer, except for longitude and latitude which are numeric (floats). All columns seem to be correct except for the timestamp. I will convert timestamp into a more readable format: Datetime.

df_train$DateTime <- as.POSIXct((df_train$TIMESTAMP), origin="1970-01-01") #Default origin time
df_validation$DateTime <- as.POSIXct((df_validation$TIMESTAMP), origin="1970-01-01") #Default origin time

any(is.na(df_train))

[1] FALSE

any(is.na(df_validation))

[1] FALSE

No null values, no need to handle them.

Initial Data exploration of the data:

hist(stack(df_train %>% select(starts_with("WAP")))$values,xlab="WAP power",main="Distribution of WAP intensity")

As expected most entries are a null reading (represented as a ‘100’). Let’s filter out these entries to get a better reading:

hist((stack(df_train %>% select(starts_with("WAP"))) %>% filter(values <100))$values,xlab="WAP power",main="Distribution of WAP intensity excluding null readings")

As expected we now have a good looking normal distribution. It is slightly skewed to the right.

hist(df_train$LONGITUDE,xlab="Longitude",main="Distribution of Longitudes")

hist(df_train$LATITUDE,xlab="Latitude",main="Distribution of Latitude")

hist(df_train$FLOOR,xlab="Floor",main="Distribution of Floors")

hist(df_train$BUILDINGID,xlab="BuildingID",main="Distribution of BuildingIDs")

hist(df_train$SPACEID,xlab="SpaceIDs",main="Distribution of SpaceIDs")

hist(df_train$RELATIVEPOSITION,xlab="Relative Position",main="Distribution of Relative Positions")

hist(df_train$USERID,xlab="User ID",main="Distribution of UserIDs")

hist(df_train$PHONEID,xlab="Phone ID",main="Distribution of Phone IDs")

Let’s confirm that the distributions are similar in the validation dataset:

hist((stack(df_validation %>% select(starts_with("WAP"))) %>% filter(values <100))$values,xlab="WAP power",main="Distribution of WAP intensity excluding null readings")

hist(df_validation$LONGITUDE,xlab="Longitude",main="Distribution of Longitudes")

hist(df_validation$LATITUDE,xlab="Latitude",main="Distribution of Latitude")

hist(df_validation$FLOOR,xlab="Floor",main="Distribution of Floors")

hist(df_validation$BUILDINGID,xlab="BuildingID",main="Distribution of BuildingIDs")

hist(df_validation$SPACEID,xlab="SpaceIDs",main="Distribution of SpaceIDs")

hist(df_validation$RELATIVEPOSITION,xlab="Relative Position",main="Distribution of Relative Positions")

hist(df_validation$USERID,xlab="User ID",main="Distribution of UserIDs")

hist(df_validation$PHONEID,xlab="Phone ID",main="Distribution of Phone IDs")

The distributions are quite similar, the exceptions are in the SPACEID, RELATIVEPOSITION and USERID where the validation dataset is constant throughout. We will confirm this below:

table(df_validation$SPACEID)

   0 
1111 

table(df_validation$RELATIVEPOSITION)

   0 
1111 

table(df_validation$USERID)

   0 
1111 

Ye, as expected all are null.

2nd round of Preprocessing the data:

Remove variables without any variation I noticed that many variables haven’t got any variation. It is useless to incorporate these features in any model as they won’t add any new information. Therefore, I will identify and later remove these variables.

constant_variables <- names(df_train[, sapply(df_train, function(v) var(v, na.rm=TRUE)==0)])
df_train <- df_train[,sapply(df_train, function(v) var(v, na.rm=TRUE)!=0)]
constant_variables

 [1] "WAP003" "WAP004" "WAP092" "WAP093" "WAP094" "WAP095" "WAP152" "WAP158" "WAP159" "WAP160" "WAP215" "WAP217" "WAP226" "WAP227"
[15] "WAP238" "WAP239" "WAP240" "WAP241" "WAP242" "WAP243" "WAP244" "WAP245" "WAP246" "WAP247" "WAP254" "WAP293" "WAP296" "WAP301"
[29] "WAP303" "WAP304" "WAP307" "WAP333" "WAP349" "WAP353" "WAP360" "WAP365" "WAP416" "WAP419" "WAP423" "WAP429" "WAP433" "WAP438"
[43] "WAP441" "WAP442" "WAP444" "WAP445" "WAP451" "WAP458" "WAP482" "WAP485" "WAP487" "WAP488" "WAP491" "WAP497" "WAP520"

Sampling As mentioned in the Plan of attack, the dataset is too large. Therefore, I will utilize a random subset of the data for the machine learning portion of this project.

set.seed(42) #Set seed to ensure reproducibility
df_sample_train <- df_train[sample(nrow(df_train), 2500),]

constant_variables <- names(df_sample_train[, sapply(df_sample_train, function(v) var(v, na.rm=TRUE)==0)])
df_sample_train <- df_sample_train[,sapply(df_sample_train, function(v) var(v, na.rm=TRUE)!=0)]
constant_variables

 [1] "WAP079" "WAP153" "WAP190" "WAP197" "WAP200" "WAP201" "WAP202" "WAP205" "WAP208" "WAP209" "WAP210" "WAP211" "WAP212" "WAP213"
[15] "WAP216" "WAP221" "WAP231" "WAP235" "WAP250" "WAP251" "WAP252" "WAP266" "WAP283" "WAP297" "WAP298" "WAP321" "WAP339" "WAP352"
[29] "WAP357" "WAP358" "WAP361" "WAP373" "WAP378" "WAP395" "WAP406" "WAP407" "WAP408" "WAP414" "WAP425" "WAP427" "WAP431" "WAP440"
[43] "WAP446" "WAP448" "WAP450" "WAP463" "WAP464" "WAP469" "WAP470" "WAP471" "WAP472" "WAP474" "WAP475" "WAP477" "WAP490" "WAP507"
[57] "WAP510"

ML Modeling

Felice recomended to forecast in cascade, firstly classify the easiest parameters (such as building; floor; inside or out…) and then make a regression for location (longitude and latitude).

Let’s do that.

The easiest parameter seems to be the relative position (in or out), then the Building ID and finally the floor. Having these 3 parameters it will hopefully be easy to infer SpaceID through a last classification model.

Relative Position

First of all let’s define the usable features and the target for this model:

df_train_RP <- df_sample_train %>% select(starts_with("WAP"),"RELATIVEPOSITION")
#Perform factorization on target column:
df_train_RP$RELATIVEPOSITION <- as.factor(as.character(df_train_RP$RELATIVEPOSITION)) #Reconvert brand into binary column not integer.

I chose the following models because these are the ones I am most familiarized and from what I understood, provide good results right out of the bat.

nbfitControl <- trainControl(method = "repeatedcv", 
                              number = 3, # number of folds
                              repeats = 1) #the number of complete sets of folds to compute
gbmfitControl <- trainControl(method = "repeatedcv", number = 3, repeats = 1)
rffitControl <- trainControl(method = "repeatedcv", number = 3, repeats = 1)

Because this dataset is slightly unbalanced, I will attempt to train according to the kappa metric instead of accuracy. (Practically, Cohen’s kappa removes the possibility of the classifier and a random guess agreeing and measures the number of predictions it makes that cannot be explained by a random guess. Furthermore, Cohen’s kappa tries to correct the evaluation bias by taking into account the correct classification by a random guess.)

Let’s train each of the 3 models with the training dataset:

nbfit_RP <- train(RELATIVEPOSITION~., #y/target
                 data = df_train_RP, #X/features
                 method = "nb", #ML algorithm
                 trControl=nbfitControl, #Apply CV to the training
                 tuneLength = 2, # Number of levels for each tuning parameters that should be generated.
                )

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observation 417Numerical 0 probability for all classes with observation 418Numerical 0 probability for all classes with observation 419Numerical 0 probability for all classes with observation 420Numerical 0 probability for all classes with observation 421Numerical 0 probability for all classes with observation 422Numerical 0 probability for all classes with observation 423Numerical 0 probability for all classes with observation 424Numerical 0 probability for all classes with observation 425Numerical 0 probability for all classes with observation 426Numerical 0 probability for all classes with observation 427Numerical 0 probability for all classes with observation 428Numerical 0 probability for all classes with observation 429Numerical 0 probability for all classes with observation 430Numerical 0 probability for all classes with observation 431Numerical 0 probability for all classes with observation 432Numerical 0 probability for all classes with observation 433Numerical 0 probability for all classes with observation 434Numerical 0 probability for all classes with observation 435Numerical 0 probability for all classes with observation 436Numerical 0 probability for all classes with observation 437Numerical 0 probability for all classes with observation 438Numerical 0 probability for all classes with observation 439Numerical 0 probability for all classes with observation 440Numerical 0 probability for all classes with observation 441Numerical 0 probability for all classes with observation 442Numerical 0 probability for all classes with observation 443Numerical 0 probability for all classes with observation 444Numerical 0 probability for all classes with observation 445Numerical 0 probability for all classes with observation 446Numerical 0 probability for all classes with observation 447Numerical 0 probability for all classes with observation 448Numerical 0 probability for all classes with observation 449Numerical 0 probability for all classes with observation 450Numerical 0 probability for all classes with observation 451Numerical 0 probability for all classes with observation 452Numerical 0 probability for all classes with observation 453Numerical 0 probability for all classes with observation 454Numerical 0 probability for all classes with observation 455Numerical 0 probability for all classes with observation 456Numerical 0 probability for all classes with observation 457Numerical 0 probability for all classes with observation 458Numerical 0 probability for all classes with observation 459Numerical 0 probability for all classes with observation 460Numerical 0 probability for all classes with observation 461Numerical 0 probability for all classes with observation 462Numerical 0 probability for all classes with observation 463Numerical 0 probability for all classes with observation 464Numerical 0 probability for all classes with observation 465Numerical 0 probability for all classes with observation 466Numerical 0 probability for all classes with observation 467Numerical 0 probability for all classes with observation 468Numerical 0 probability for all classes with observation 469Numerical 0 probability for all classes with observation 470Numerical 0 probability for all classes with observation 471Numerical 0 probability for all classes with observation 472Numerical 0 probability for all classes with observation 473Numerical 0 probability for all classes with observation 474Numerical 0 probability for all classes with observation 475Numerical 0 probability for all classes with observation 476Numerical 0 probability for all classes with observation 477Numerical 0 probability for all classes with observation 478Numerical 0 probability for all classes with observation 479Numerical 0 probability for all classes with observation 480Numerical 0 probability for all classes with observation 481Numerical 0 probability for all classes with observation 482Numerical 0 probability for all classes with observation 483Numerical 0 probability for all classes with observation 484Numerical 0 probability for all classes with observation 485Numerical 0 probability for all classes with observation 486Numerical 0 probability for all classes with observation 487Numerical 0 probability for all classes with observation 488Numerical 0 probability for all classes with observation 489Numerical 0 probability for all classes with observation 490Numerical 0 probability for all classes with observation 491Numerical 0 probability for all classes with observation 492Numerical 0 probability for all classes with observation 493Numerical 0 probability for all classes with observation 494Numerical 0 probability for all classes with observation 495Numerical 0 probability for all classes with observation 496Numerical 0 probability for all classes with observation 497Numerical 0 probability for all classes with observation 498Numerical 0 probability for all classes with observation 499Numerical 0 probability for all classes with observation 500Numerical 0 probability for all classes with observation 501Numerical 0 probability for all classes with observation 502Numerical 0 probability for all classes with observation 503Numerical 0 probability for all classes with observation 504Numerical 0 probability for all classes with observation 505Numerical 0 probability for all classes with observation 506Numerical 0 probability for all classes with observation 507Numerical 0 probability for all classes with observation 508Numerical 0 probability for all classes with observation 509Numerical 0 probability for all classes with observation 510Numerical 0 probability for all classes with observation 511Numerical 0 probability for all classes with observation 512Numerical 0 probability for all classes with observation 513Numerical 0 probability for all classes with observation 514Numerical 0 probability for all classes with observation 515Numerical 0 probability for all classes with observation 516Numerical 0 probability for all classes with observation 517Numerical 0 probability for all classes with observation 518Numerical 0 probability for all classes with observation 519Numerical 0 probability for all classes with observation 520Numerical 0 probability for all classes with observation 521Numerical 0 probability for all classes with observation 522Numerical 0 probability for all classes with observation 523Numerical 0 probability for all classes with observation 524Numerical 0 probability for all classes with observation 525Numerical 0 probability for all classes with observation 526Numerical 0 probability for all classes with observation 527Numerical 0 probability for all classes with observation 528Numerical 0 probability for all classes with observation 529Numerical 0 probability for all classes with observation 530Numerical 0 probability for all classes with observation 531Numerical 0 probability for all classes with observation 532Numerical 0 probability for all classes with observation 533Numerical 0 probability for all classes with observation 534Numerical 0 probability for all classes with observation 535Numerical 0 probability for all classes with observation 536Numerical 0 probability for all classes with observation 537Numerical 0 probability for all classes with observation 538Numerical 0 probability for all classes with observation 539Numerical 0 probability for all classes with observation 540Numerical 0 probability for all classes with observation 541Numerical 0 probability for all classes with observation 542Numerical 0 probability for all classes with observation 543Numerical 0 probability for all classes with observation 544Numerical 0 probability for all classes with observation 545Numerical 0 probability for all classes with observation 546Numerical 0 probability for all classes with observation 547Numerical 0 probability for all classes with observation 548Numerical 0 probability for all classes with observation 549Numerical 0 probability for all classes with observation 550Numerical 0 probability for all classes with observation 551Numerical 0 probability for all classes with observation 552Numerical 0 probability for all classes with observation 553Numerical 0 probability for all classes with observation 554Numerical 0 probability for all classes with observation 555Numerical 0 probability for all classes with observation 556Numerical 0 probability for all classes with observation 557Numerical 0 probability for all classes with observation 558Numerical 0 probability for all classes with observation 559Numerical 0 probability for all classes with observation 560Numerical 0 probability for all classes with observation 561Numerical 0 probability for all classes with observation 562Numerical 0 probability for all classes with observation 563Numerical 0 probability for all classes with observation 564Numerical 0 probability for all classes with observation 565Numerical 0 probability for all classes with observation 566Numerical 0 probability for all classes with observation 567Numerical 0 probability for all classes with observation 568Numerical 0 probability for all classes with observation 569Numerical 0 probability for all classes with observation 570Numerical 0 probability for all classes with observation 571Numerical 0 probability for all classes with observation 572Numerical 0 probability for all classes with observation 573Numerical 0 probability for all classes with observation 574Numerical 0 probability for all classes with observation 575Numerical 0 probability for all classes with observation 576Numerical 0 probability for all classes with observation 577Numerical 0 probability for all classes with observation 578Numerical 0 probability for all classes with observation 579Numerical 0 probability for all classes with observation 580Numerical 0 probability for all classes with observation 581Numerical 0 probability for all classes with observation 582Numerical 0 probability for all classes with observation 583Numerical 0 probability for all classes with observation 584Numerical 0 probability for all classes with observation 585Numerical 0 probability for all classes with observation 586Numerical 0 probability for all classes with observation 587Numerical 0 probability for all classes with observation 588Numerical 0 probability for all classes with observation 589Numerical 0 probability for all classes with observation 590Numerical 0 probability for all classes with observation 591Numerical 0 probability for all classes with observation 592Numerical 0 probability for all classes with observation 593Numerical 0 probability for all classes with observation 594Numerical 0 probability for all classes with observation 595Numerical 0 probability for all classes with observation 596Numerical 0 probability for all classes with observation 597Numerical 0 probability for all classes with observation 598Numerical 0 probability for all classes with observation 599Numerical 0 probability for all classes with observation 600Numerical 0 probability for all classes with observation 601Numerical 0 probability for all classes with observation 602Numerical 0 probability for all classes with observation 603Numerical 0 probability for all classes with observation 604Numerical 0 probability for all classes with observation 605Numerical 0 probability for all classes with observation 606Numerical 0 probability for all classes with observation 607Numerical 0 probability for all classes with observation 608Numerical 0 probability for all classes with observation 609Numerical 0 probability for all classes with observation 610Numerical 0 probability for all classes with observation 611Numerical 0 probability for all classes with observation 612Numerical 0 probability for all classes with observation 613Numerical 0 probability for all classes with observation 614Numerical 0 probability for all classes with observation 615Numerical 0 probability for all classes with observation 616Numerical 0 probability for all classes with observation 617Numerical 0 probability for all classes with observation 618Numerical 0 probability for all classes with observation 619Numerical 0 probability for all classes with observation 620Numerical 0 probability for all classes with observation 621Numerical 0 probability for all classes with observation 622Numerical 0 probability for all classes with observation 623Numerical 0 probability for all classes with observation 624Numerical 0 probability for all classes with observation 625Numerical 0 probability for all classes with observation 626Numerical 0 probability for all classes with observation 627Numerical 0 probability for all classes with observation 628Numerical 0 probability for all classes with observation 629Numerical 0 probability for all classes with observation 630Numerical 0 probability for all classes with observation 631Numerical 0 probability for all classes with observation 632Numerical 0 probability for all classes with observation 633Numerical 0 probability for all classes with observation 634Numerical 0 probability for all classes with observation 635Numerical 0 probability for all classes with observation 636Numerical 0 probability for all classes with observation 637Numerical 0 probability for all classes with observation 638Numerical 0 probability for all classes with observation 639Numerical 0 probability for all classes with observation 640Numerical 0 probability for all classes with observation 641Numerical 0 probability for all classes with observation 642Numerical 0 probability for all classes with observation 643Numerical 0 probability for all classes with observation 644Numerical 0 probability for all classes with observation 645Numerical 0 probability for all classes with observation 646Numerical 0 probability for all classes with observation 647Numerical 0 probability for all classes with observation 648Numerical 0 probability for all classes with observation 649Numerical 0 probability for all classes with observation 650Numerical 0 probability for all classes with observation 651Numerical 0 probability for all classes with observation 652Numerical 0 probability for all classes with observation 653Numerical 0 probability for all classes with observation 654Numerical 0 probability for all classes with observation 655Numerical 0 probability for all classes with observation 656Numerical 0 probability for all classes with observation 657Numerical 0 probability for all classes with observation 658Numerical 0 probability for all classes with observation 659Numerical 0 probability for all classes with observation 660Numerical 0 probability for all classes with observation 661Numerical 0 probability for all classes with observation 662Numerical 0 probability for all classes with observation 663Numerical 0 probability for all classes with observation 664Numerical 0 probability for all classes with observation 665Numerical 0 probability for all classes with observation 666Numerical 0 probability for all classes with observation 667Numerical 0 probability for all classes with observation 668Numerical 0 probability for all classes with observation 669Numerical 0 probability for all classes with observation 670Numerical 0 probability for all classes with observation 671Numerical 0 probability for all classes with observation 672Numerical 0 probability for all classes with observation 673Numerical 0 probability for all classes with observation 674Numerical 0 probability for all classes with observation 675Numerical 0 probability for all classes with observation 676Numerical 0 probability for all classes with observation 677Numerical 0 probability for all classes with observation 678Numerical 0 probability for all classes with observation 679Numerical 0 probability for all classes with observation 680Numerical 0 probability for all classes with observation 681Numerical 0 probability for all classes with observation 682Numerical 0 probability for all classes with observation 683Numerical 0 probability for all classes with observation 684Numerical 0 probability for all classes with observation 685Numerical 0 probability for all classes with observation 686Numerical 0 probability for all classes with observation 687Numerical 0 probability for all classes with observation 688Numerical 0 probability for all classes with observation 689Numerical 0 probability for all classes with observation 690Numerical 0 probability for all classes with observation 691Numerical 0 probability for all classes with observation 692Numerical 0 probability for all classes with observation 693Numerical 0 probability for all classes with observation 694Numerical 0 probability for all classes with observation 695Numerical 0 probability for all classes with observation 696Numerical 0 probability for all classes with observation 697Numerical 0 probability for all classes with observation 698Numerical 0 probability for all classes with observation 699Numerical 0 probability for all classes with observation 700Numerical 0 probability for all classes with observation 701Numerical 0 probability for all classes with observation 702Numerical 0 probability for all classes with observation 703Numerical 0 probability for all classes with observation 704Numerical 0 probability for all classes with observation 705Numerical 0 probability for all classes with observation 706Numerical 0 probability for all classes with observation 707Numerical 0 probability for all classes with observation 708Numerical 0 probability for all classes with observation 709Numerical 0 probability for all classes with observation 710Numerical 0 probability for all classes with observation 711Numerical 0 probability for all classes with observation 712Numerical 0 probability for all classes with observation 713Numerical 0 probability for all classes with observation 714Numerical 0 probability for all classes with observation 715Numerical 0 probability for all classes with observation 716Numerical 0 probability for all classes with observation 717Numerical 0 probability for all classes with observation 718Numerical 0 probability for all classes with observation 719Numerical 0 probability for all classes with observation 720Numerical 0 probability for all classes with observation 721Numerical 0 probability for all classes with observation 722Numerical 0 probability for all classes with observation 723Numerical 0 probability for all classes with observation 724Numerical 0 probability for all classes with observation 725Numerical 0 probability for all classes with observation 726Numerical 0 probability for all classes with observation 727Numerical 0 probability for all classes with observation 728Numerical 0 probability for all classes with observation 729Numerical 0 probability for all classes with observation 730Numerical 0 probability for all classes with observation 731Numerical 0 probability for all classes with observation 732Numerical 0 probability for all classes with observation 733Numerical 0 probability for all classes with observation 734Numerical 0 probability for all classes with observation 735Numerical 0 probability for all classes with observation 736Numerical 0 probability for all classes with observation 737Numerical 0 probability for all classes with observation 738Numerical 0 probability for all classes with observation 739Numerical 0 probability for all classes with observation 740Numerical 0 probability for all classes with observation 741Numerical 0 probability for all classes with observation 742Numerical 0 probability for all classes with observation 743Numerical 0 probability for all classes with observation 744Numerical 0 probability for all classes with observation 745Numerical 0 probability for all classes with observation 746Numerical 0 probability for all classes with observation 747Numerical 0 probability for all classes with observation 748Numerical 0 probability for all classes with observation 749Numerical 0 probability for all classes with observation 750Numerical 0 probability for all classes with observation 751Numerical 0 probability for all classes with observation 752Numerical 0 probability for all classes with observation 753Numerical 0 probability for all classes with observation 754Numerical 0 probability for all classes with observation 755Numerical 0 probability for all classes with observation 756Numerical 0 probability for all classes with observation 757Numerical 0 probability for all classes with observation 758Numerical 0 probability for all classes with observation 759Numerical 0 probability for all classes with observation 760Numerical 0 probability for all classes with observation 761Numerical 0 probability for all classes with observation 762Numerical 0 probability for all classes with observation 763Numerical 0 probability for all classes with observation 764Numerical 0 probability for all classes with observation 765Numerical 0 probability for all classes with observation 766Numerical 0 probability for all classes with observation 767Numerical 0 probability for all classes with observation 768Numerical 0 probability for all classes with observation 769Numerical 0 probability for all classes with observation 770Numerical 0 probability for all classes with observation 771Numerical 0 probability for all classes with observation 772Numerical 0 probability for all classes with observation 773Numerical 0 probability for all classes with observation 774Numerical 0 probability for all classes with observation 775Numerical 0 probability for all classes with observation 776Numerical 0 probability for all classes with observation 777Numerical 0 probability for all classes with observation 778Numerical 0 probability for all classes with observation 779Numerical 0 probability for all classes with observation 780Numerical 0 probability for all classes with observation 781Numerical 0 probability for all classes with observation 782Numerical 0 probability for all classes with observation 783Numerical 0 probability for all classes with observation 784Numerical 0 probability for all classes with observation 785Numerical 0 probability for all classes with observation 786Numerical 0 probability for all classes with observation 787Numerical 0 probability for all classes with observation 788Numerical 0 probability for all classes with observation 789Numerical 0 probability for all classes with observation 790Numerical 0 probability for all classes with observation 791Numerical 0 probability for all classes with observation 792Numerical 0 probability for all classes with observation 793Numerical 0 probability for all classes with observation 794Numerical 0 probability for all classes with observation 795Numerical 0 probability for all classes with observation 796Numerical 0 probability for all classes with observation 797Numerical 0 probability for all classes with observation 798Numerical 0 probability for all classes with observation 799Numerical 0 probability for all classes with observation 800Numerical 0 probability for all classes with observation 801Numerical 0 probability for all classes with observation 802Numerical 0 probability for all classes with observation 803Numerical 0 probability for all classes with observation 804Numerical 0 probability for all classes with observation 805Numerical 0 probability for all classes with observation 806Numerical 0 probability for all classes with observation 807Numerical 0 probability for all classes with observation 808Numerical 0 probability for all classes with observation 809Numerical 0 probability for all classes with observation 810Numerical 0 probability for all classes with observation 811Numerical 0 probability for all classes with observation 812Numerical 0 probability for all classes with observation 813Numerical 0 probability for all classes with observation 814Numerical 0 probability for all classes with observation 815Numerical 0 probability for all classes with observation 816Numerical 0 probability for all classes with observation 817Numerical 0 probability for all classes with observation 818Numerical 0 probability for all classes with observation 819Numerical 0 probability for all classes with observation 820Numerical 0 probability for all classes with observation 821Numerical 0 probability for all classes with observation 822Numerical 0 probability for all classes with observation 823Numerical 0 probability for all classes with observation 824Numerical 0 probability for all classes with observation 825Numerical 0 probability for all classes with observation 826Numerical 0 probability for all classes with observation 827Numerical 0 probability for all classes with observation 828Numerical 0 probability for all classes with observation 829Numerical 0 probability for all classes with observation 830Numerical 0 probability for all classes with observation 831Numerical 0 probability for all classes with observation 832Numerical 0 probability for all classes with observation 833Numerical 0 probability for all classes with observation 834model fit failed for Fold1.Rep1: usekernel=FALSE, fL=0, adjust=1 Error in NaiveBayes.default(x, y, usekernel = FALSE, fL = param$fL, ...) : 
  Zero variances for at least one class in variables: WAP001, WAP002, WAP005, WAP009, WAP017, WAP018, WAP019, WAP020, WAP025, WAP026, WAP027, WAP028, WAP031, WAP032, WAP033, WAP034, WAP043, WAP044, WAP047, WAP048, WAP049, WAP050, WAP051, WAP052, WAP055, WAP056, WAP057, WAP058, WAP071, WAP072, WAP075, WAP076, WAP080, WAP081, WAP086, WAP100, WAP133, WAP142, WAP143, WAP154, WAP157, WAP162, WAP163, WAP193, WAP194, WAP195, WAP196, WAP198, WAP206, WAP207, WAP214, WAP219, WAP220, WAP224, WAP228, WAP264, WAP265, WAP267, WAP269, WAP270, WAP271, WAP272, WAP273, WAP275, WAP276, WAP280, WAP281, WAP285, WAP287, WAP290, WAP291, WAP292, WAP294, WAP299, WAP300, WAP302, WAP305, WAP306, WAP308, WAP309, WAP319, WAP320, WAP322, WAP324, WAP325, WAP326, WAP327, WAP328, WAP330, WAP331, WAP336, WAP337, WAP341, WAP343, WAP345, WAP346, WAP347, WAP348, WAP350, WAP354, WAP355, WAP356, WAP359, WAP362, WAP363, WAP364, WAP376, WAP377, WAP379, WAP381, WAP382, WAP383, WAP384, WAP385, WAP387, WAP388, WAP392, WAP393, WAP397, WAP399, WAP402, WAP403, WAP404, WAP409, WAP410, WAP411, WAP412, WAP413, WAP415, WAP417, WAP420, WAP421, WAP422, WAP424, WAP426, WAP430, WAP434, WAP436, WAP437, WAP443, WAP447, WAP452, WAP454, WAP457, WAP459, WAP461, WAP462, WAP466, WAP467, WAP468, WAP476, WAP493, WAP494, WAP499, WAP500, WAP505, WAP506, WAP509, WAP512, WAP514, WAP515, WAP518, WAP519
Numerical 0 probability for all classes with observation 1Numerical 0 probability for all classes with observation 2Numerical 0 probability for all classes with observation 3Numerical 0 probability for all classes with observation 4Numerical 0 probability for all classes with observation 5Numerical 0 probability for all classes with observation 6Numerical 0 probability for all classes with observation 7Numerical 0 probability for all classes with observation 8Numerical 0 probability for all classes with observation 9Numerical 0 probability for all classes with observation 10Numerical 0 probability for all classes with observation 11Numerical 0 probability for all classes with observation 12Numerical 0 probability for all classes with observation 13Numerical 0 probability for all classes with observation 14Numerical 0 probability for all classes with observation 15Numerical 0 probability for all classes with observation 16Numerical 0 probability for all classes with observation 17Numerical 0 probability for all classes with observation 18Numerical 0 probability for all classes with observation 19Numerical 0 probability for all classes with observation 20Numerical 0 probability for all classes with observation 21Numerical 0 probability for all classes with observation 22Numerical 0 probability for all classes with observation 23Numerical 0 probability for all classes with observation 24Numerical 0 probability for all classes with observation 25Numerical 0 probability for all classes with observation 26Numerical 0 probability for all classes with observation 27Numerical 0 probability for all classes with observation 28Numerical 0 probability for all classes with observation 29Numerical 0 probability for all classes with observation 30Numerical 0 probability for all classes with observation 31Numerical 0 probability for all classes with observation 32Numerical 0 probability for all classes with observation 33Numerical 0 probability for all classes with observation 34Numerical 0 probability for all classes with observation 35Numerical 0 probability for all classes with observation 36Numerical 0 probability for all classes with observation 37Numerical 0 probability for all classes with observation 38Numerical 0 probability for all classes with observation 39Numerical 0 probability for all classes with observation 40Numerical 0 probability for all classes with observation 41Numerical 0 probability for all classes with observation 42Numerical 0 probability for all classes with observation 43Numerical 0 probability for all classes with observation 44Numerical 0 probability for all classes with observation 45Numerical 0 probability for all classes with observation 46Numerical 0 probability for all classes with observation 47Numerical 0 probability for all classes with observation 48Numerical 0 probability for all classes with observation 49Numerical 0 probability for all classes with observation 50Numerical 0 probability for all classes with observation 51Numerical 0 probability for all classes with observation 52Numerical 0 probability for all classes with observation 53Numerical 0 probability for all classes with observation 54Numerical 0 probability for all classes with observation 55Numerical 0 probability for all classes with observation 56Numerical 0 probability for all classes with observation 57Numerical 0 probability for all classes with observation 58Numerical 0 probability for all classes with observation 59Numerical 0 probability for all classes with observation 60Numerical 0 probability for all classes with observation 61Numerical 0 probability for all classes with observation 62Numerical 0 probability for all classes with observation 63Numerical 0 probability for all classes with observation 64Numerical 0 probability for all classes with observation 65Numerical 0 probability for all classes with observation 66Numerical 0 probability for all classes with observation 67Numerical 0 probability for all classes with observation 68Numerical 0 probability for all classes with observation 69Numerical 0 probability for all classes with observation 70Numerical 0 probability for all classes with observation 71Numerical 0 probability for all classes with observation 72Numerical 0 probability for all classes with observation 73Numerical 0 probability for all classes with observation 74Numerical 0 probability for all classes with observation 75Numerical 0 probability for all classes with observation 76Numerical 0 probability for all classes with observation 77Numerical 0 probability for all classes with observation 78Numerical 0 probability for all classes with observation 79Numerical 0 probability for all classes with observation 80Numerical 0 probability for all classes with observation 81Numerical 0 probability for all classes with observation 82Numerical 0 probability for all classes with observation 83Numerical 0 probability for all classes with observation 84Numerical 0 probability for all classes with observation 85Numerical 0 probability for all classes with observation 86Numerical 0 probability for all classes with observation 87Numerical 0 probability for all classes with observation 88Numerical 0 probability for all classes with observation 89Numerical 0 probability for all classes with observation 90Numerical 0 probability for all classes with observation 91Numerical 0 probability for all classes with observation 92Numerical 0 probability for all classes with observation 93Numerical 0 probability for all classes with observation 94Numerical 0 probability for all classes with observation 95Numerical 0 probability for all classes with observation 96Numerical 0 probability for all classes with observation 97Numerical 0 probability for all classes with observation 98Numerical 0 probability for all classes with observation 99Numerical 0 probability for all classes with observation 100Numerical 0 probability for all classes with observation 101Numerical 0 probability for all classes with observation 102Numerical 0 probability for all classes with observation 103Numerical 0 probability for all classes with observation 104Numerical 0 probability for all classes with observation 105Numerical 0 probability for all classes with observation 106Numerical 0 probability for all classes with observation 107Numerical 0 probability for all classes with observation 108Numerical 0 probability for all classes with observation 109Numerical 0 probability for all classes with observation 110Numerical 0 probability for all classes with observation 111Numerical 0 probability for all classes with observation 112Numerical 0 probability for all classes with observation 113Numerical 0 probability for all classes with observation 114Numerical 0 probability for all classes with observation 115Numerical 0 probability for all classes with observation 116Numerical 0 probability for all classes with observation 117Numerical 0 probability for all classes with observation 118Numerical 0 probability for all classes with observation 119Numerical 0 probability for all classes with observation 120Numerical 0 probability for all classes with observation 121Numerical 0 probability for all classes with observation 122Numerical 0 probability for all classes with observation 123Numerical 0 probability for all classes with observation 124Numerical 0 probability for all classes with observation 125Numerical 0 probability for all classes with observation 126Numerical 0 probability for all classes with observation 127Numerical 0 probability for all classes with observation 128Numerical 0 probability for all classes with observation 129Numerical 0 probability for all classes with observation 130Numerical 0 probability for all classes with observation 131Numerical 0 probability for all classes with observation 132Numerical 0 probability for all classes with observation 133Numerical 0 probability for all classes with observation 134Numerical 0 probability for all classes with observation 135Numerical 0 probability for all classes with observation 136Numerical 0 probability for all classes with observation 137Numerical 0 probability for all classes with observation 138Numerical 0 probability for all classes with observation 139Numerical 0 probability for all classes with observation 140Numerical 0 probability for all classes with observation 141Numerical 0 probability for all classes with observation 142Numerical 0 probability for all classes with observation 143Numerical 0 probability for all classes with observation 144Numerical 0 probability for all classes with observation 145Numerical 0 probability for all classes with observation 146Numerical 0 probability for all classes with observation 147Numerical 0 probability for all classes with observation 148Numerical 0 probability for all classes with observation 149Numerical 0 probability for all classes with observation 150Numerical 0 probability for all classes with observation 151Numerical 0 probability for all classes with observation 152Numerical 0 probability for all classes with observation 153Numerical 0 probability for all classes with observation 154Numerical 0 probability for all classes with observation 155Numerical 0 probability for all classes with observation 156Numerical 0 probability for all classes with observation 157Numerical 0 probability for all classes with observation 158Numerical 0 probability for all classes with observation 159Numerical 0 probability for all classes with observation 160Numerical 0 probability for all classes with observation 161Numerical 0 probability for all classes with observation 162Numerical 0 probability for all classes with observation 163Numerical 0 probability for all classes with observation 164Numerical 0 probability for all classes with observation 165Numerical 0 probability for all classes with observation 166Numerical 0 probability for all classes with observation 167Numerical 0 probability for all classes with observation 168Numerical 0 probability for all classes with observation 169Numerical 0 probability for all classes with observation 170Numerical 0 probability for all classes with observation 171Numerical 0 probability for all classes with observation 172Numerical 0 probability for all classes with observation 173Numerical 0 probability for all classes with observation 174Numerical 0 probability for all classes with observation 175Numerical 0 probability for all classes with observation 176Numerical 0 probability for all classes with observation 177Numerical 0 probability for all classes with observation 178Numerical 0 probability for all classes with observation 179Numerical 0 probability for all classes with observation 180Numerical 0 probability for all classes with observation 181Numerical 0 probability for all classes with observation 182Numerical 0 probability for all classes with observation 183Numerical 0 probability for all classes with observation 184Numerical 0 probability for all classes with observation 185Numerical 0 probability for all classes with observation 186Numerical 0 probability for all classes with observation 187Numerical 0 probability for all classes with observation 188Numerical 0 probability for all classes with observation 189Numerical 0 probability for all classes with observation 190Numerical 0 probability for all classes with observation 191Numerical 0 probability for all classes with observation 192Numerical 0 probability for all classes with observation 193Numerical 0 probability for all classes with observation 194Numerical 0 probability for all classes with observation 195Numerical 0 probability for all classes with observation 196Numerical 0 probability for all classes with observation 197Numerical 0 probability for all classes with observation 198Numerical 0 probability for all classes with observation 199Numerical 0 probability for all classes with observation 200Numerical 0 probability for all classes with observation 201Numerical 0 probability for all classes with observation 202Numerical 0 probability for all classes with observation 203Numerical 0 probability for all classes with observation 204Numerical 0 probability for all classes with observation 205Numerical 0 probability for all classes with observation 206Numerical 0 probability for all classes with observation 207Numerical 0 probability for all classes with observation 208Numerical 0 probability for all classes with observation 209Numerical 0 probability for all classes with observation 210Numerical 0 probability for all classes with observation 211Numerical 0 probability for all classes with observation 212Numerical 0 probability for all classes with observation 213Numerical 0 probability for all classes with observation 214Numerical 0 probability for all classes with observation 215Numerical 0 probability for all classes with observation 216Numerical 0 probability for all classes with observation 217Numerical 0 probability for all classes with observation 218Numerical 0 probability for all classes with observation 219Numerical 0 probability for all classes with observation 220Numerical 0 probability for all classes with observation 221Numerical 0 probability for all classes with observation 222Numerical 0 probability for all classes with observation 223Numerical 0 probability for all classes with observation 224Numerical 0 probability for all classes with observation 225Numerical 0 probability for all classes with observation 226Numerical 0 probability for all classes with observation 227Numerical 0 probability for all classes with observation 228Numerical 0 probability for all classes with observation 229Numerical 0 probability for all classes with observation 230Numerical 0 probability for all classes with observation 231Numerical 0 probability for all classes with observation 232Numerical 0 probability for all classes with observation 233Numerical 0 probability for all classes with observation 234Numerical 0 probability for all classes with observation 235Numerical 0 probability for all classes with observation 236Numerical 0 probability for all classes with observation 237Numerical 0 probability for all classes with observation 238Numerical 0 probability for all classes with observation 239Numerical 0 probability for all classes with observation 240Numerical 0 probability for all classes with observation 241Numerical 0 probability for all classes with observation 242Numerical 0 probability for all classes with observation 243Numerical 0 probability for all classes with observation 244Numerical 0 probability for all classes with observation 245Numerical 0 probability for all classes with observation 246Numerical 0 probability for all classes with observation 247Numerical 0 probability for all classes with observation 248Numerical 0 probability for all classes with observation 249Numerical 0 probability for all classes with observation 250Numerical 0 probability for all classes with observation 251Numerical 0 probability for all classes with observation 252Numerical 0 probability for all classes with observation 253Numerical 0 probability for all classes with observation 254Numerical 0 probability for all classes with observation 255Numerical 0 probability for all classes with observation 256Numerical 0 probability for all classes with observation 257Numerical 0 probability for all classes with observation 258Numerical 0 probability for all classes with observation 259Numerical 0 probability for all classes with observation 260Numerical 0 probability for all classes with observation 261Numerical 0 probability for all classes with observation 262Numerical 0 probability for all classes with observation 263Numerical 0 probability for all classes with observation 264Numerical 0 probability for all classes with observation 265Numerical 0 probability for all classes with observation 266Numerical 0 probability for all classes with observation 267Numerical 0 probability for all classes with observation 268Numerical 0 probability for all classes with observation 269Numerical 0 probability for all classes with observation 270Numerical 0 probability for all classes with observation 271Numerical 0 probability for all classes with observation 272Numerical 0 probability for all classes with observation 273Numerical 0 probability for all classes with observation 274Numerical 0 probability for all classes with observation 275Numerical 0 probability for all classes with observation 276Numerical 0 probability for all classes with observation 277Numerical 0 probability for all classes with observation 278Numerical 0 probability for all classes with observation 279Numerical 0 probability for all classes with observation 280Numerical 0 probability for all classes with observation 281Numerical 0 probability for all classes with observation 282Numerical 0 probability for all classes with observation 283Numerical 0 probability for all classes with observation 284Numerical 0 probability for all classes with observation 285Numerical 0 probability for all classes with observation 286Numerical 0 probability for all classes with observation 287Numerical 0 probability for all classes with observation 288Numerical 0 probability for all classes with observation 289Numerical 0 probability for all classes with observation 290Numerical 0 probability for all classes with observation 291Numerical 0 probability for all classes with observation 292Numerical 0 probability for all classes with observation 293Numerical 0 probability for all classes with observation 294Numerical 0 probability for all classes with observation 295Numerical 0 probability for all classes with observation 296Numerical 0 probability for all classes with observation 297Numerical 0 probability for all classes with observation 298Numerical 0 probability for all classes with observation 299Numerical 0 probability for all classes with observation 300Numerical 0 probability for all classes with observation 301Numerical 0 probability for all classes with observation 302Numerical 0 probability for all classes with observation 303Numerical 0 probability for all classes with observation 304Numerical 0 probability for all classes with observation 305Numerical 0 probability for all classes with observation 306Numerical 0 probability for all classes with observation 307Numerical 0 probability for all classes with observation 308Numerical 0 probability for all classes with observation 309Numerical 0 probability for all classes with observation 310Numerical 0 probability for all classes with observation 311Numerical 0 probability for all classes with observation 312Numerical 0 probability for all classes with observation 313Numerical 0 probability for all classes with observation 314Numerical 0 probability for all classes with observation 315Numerical 0 probability for all classes with observation 316Numerical 0 probability for all classes with observation 317Numerical 0 probability for all classes with observation 318Numerical 0 probability for all classes with observation 319Numerical 0 probability for all classes with observation 320Numerical 0 probability for all classes with observation 321Numerical 0 probability for all classes with observation 322Numerical 0 probability for all classes with observation 323Numerical 0 probability for all classes with observation 324Numerical 0 probability for all classes with observation 325Numerical 0 probability for all classes with observation 326Numerical 0 probability for all classes with observation 327Numerical 0 probability for all classes with observation 328Numerical 0 probability for all classes with observation 329Numerical 0 probability for all classes with observation 330Numerical 0 probability for all classes with observation 331Numerical 0 probability for all classes with observation 332Numerical 0 probability for all classes with observation 333Numerical 0 probability for all classes with observation 334Numerical 0 probability for all classes with observation 335Numerical 0 probability for all classes with observation 336Numerical 0 probability for all classes with observation 337Numerical 0 probability for all classes with observation 338Numerical 0 probability for all classes with observation 339Numerical 0 probability for all classes with observation 340Numerical 0 probability for all classes with observation 341Numerical 0 probability for all classes with observation 342Numerical 0 probability for all classes with observation 343Numerical 0 probability for all classes with observation 344Numerical 0 probability for all classes with observation 345Numerical 0 probability for all classes with observation 346Numerical 0 probability for all classes with observation 347Numerical 0 probability for all classes with observation 348Numerical 0 probability for all classes with observation 349Numerical 0 probability for all classes with observation 350Numerical 0 probability for all classes with observation 351Numerical 0 probability for all classes with observation 352Numerical 0 probability for all classes with observation 353Numerical 0 probability for all classes with observation 354Numerical 0 probability for all classes with observation 355Numerical 0 probability for all classes with observation 356Numerical 0 probability for all classes with observation 357Numerical 0 probability for all classes with observation 358Numerical 0 probability for all classes with observation 359Numerical 0 probability for all classes with observation 360Numerical 0 probability for all classes with observation 361Numerical 0 probability for all classes with observation 362Numerical 0 probability for all classes with observation 363Numerical 0 probability for all classes with observation 364Numerical 0 probability for all classes with observation 365Numerical 0 probability for all classes with observation 366Numerical 0 probability for all classes with observation 367Numerical 0 probability for all classes with observation 368Numerical 0 probability for all classes with observation 369Numerical 0 probability for all classes with observation 370Numerical 0 probability for all classes with observation 371Numerical 0 probability for all classes with observation 372Numerical 0 probability for all classes with observation 373Numerical 0 probability for all classes with observation 374Numerical 0 probability for all classes with observation 375Numerical 0 probability for all classes with observation 376Numerical 0 probability for all classes with observation 377Numerical 0 probability for all classes with observation 378Numerical 0 probability for all classes with observation 379Numerical 0 probability for all classes with observation 380Numerical 0 probability for all classes with observation 381Numerical 0 probability for all classes with observation 382Numerical 0 probability for all classes with observation 383Numerical 0 probability for all classes with observation 384Numerical 0 probability for all classes with observation 385Numerical 0 probability for all classes with observation 386Numerical 0 probability for all classes with observation 387Numerical 0 probability for all classes with observation 388Numerical 0 probability for all classes with observation 389Numerical 0 probability for all classes with observation 390Numerical 0 probability for all classes with observation 391Numerical 0 probability for all classes with observation 392Numerical 0 probability for all classes with observation 393Numerical 0 probability for all classes with observation 394Numerical 0 probability for all classes with observation 395Numerical 0 probability for all classes with observation 396Numerical 0 probability for all classes with observation 397Numerical 0 probability for all classes with observation 398Numerical 0 probability for all classes with observation 399Numerical 0 probability for all classes with observation 400Numerical 0 probability for all classes with observation 401Numerical 0 probability for all classes with observation 402Numerical 0 probability for all classes with observation 403Numerical 0 probability for all classes with observation 404Numerical 0 probability for all classes with observation 405Numerical 0 probability for all classes with observation 406Numerical 0 probability for all classes with observation 407Numerical 0 probability for all classes with observation 408Numerical 0 probability for all classes with observation 409Numerical 0 probability for all classes with observation 410Numerical 0 probability for all classes with observation 411Numerical 0 probability for all classes with observation 412Numerical 0 probability for all classes with observation 413Numerical 0 probability for all classes with observation 414Numerical 0 probability for all classes with observation 415Numerical 0 probability for all classes with observation 416Numerical 0 probability for all classes with observation 417Numerical 0 probability for all classes with observation 418Numerical 0 probability for all classes with observation 419Numerical 0 probability for all classes with observation 420Numerical 0 probability for all classes with observation 421Numerical 0 probability for all classes with observation 422Numerical 0 probability for all classes with observation 423Numerical 0 probability for all classes with observation 424Numerical 0 probability for all classes with observation 425Numerical 0 probability for all classes with observation 426Numerical 0 probability for all classes with observation 427Numerical 0 probability for all classes with observation 428Numerical 0 probability for all classes with observation 429Numerical 0 probability for all classes with observation 430Numerical 0 probability for all classes with observation 431Numerical 0 probability for all classes with observation 432Numerical 0 probability for all classes with observation 433Numerical 0 probability for all classes with observation 434Numerical 0 probability for all classes with observation 435Numerical 0 probability for all classes with observation 436Numerical 0 probability for all classes with observation 437Numerical 0 probability for all classes with observation 438Numerical 0 probability for all classes with observation 439Numerical 0 probability for all classes with observation 440Numerical 0 probability for all classes with observation 441Numerical 0 probability for all classes with observation 442Numerical 0 probability for all classes with observation 443Numerical 0 probability for all classes with observation 444Numerical 0 probability for all classes with observation 445Numerical 0 probability for all classes with observation 446Numerical 0 probability for all classes with observation 447Numerical 0 probability for all classes with observation 448Numerical 0 probability for all classes with observation 449Numerical 0 probability for all classes with observation 450Numerical 0 probability for all classes with observation 451Numerical 0 probability for all classes with observation 452Numerical 0 probability for all classes with observation 453Numerical 0 probability for all classes with observation 454Numerical 0 probability for all classes with observation 455Numerical 0 probability for all classes with observation 456Numerical 0 probability for all classes with observation 457Numerical 0 probability for all classes with observation 458Numerical 0 probability for all classes with observation 459Numerical 0 probability for all classes with observation 460Numerical 0 probability for all classes with observation 461Numerical 0 probability for all classes with observation 462Numerical 0 probability for all classes with observation 463Numerical 0 probability for all classes with observation 464Numerical 0 probability for all classes with observation 465Numerical 0 probability for all classes with observation 466Numerical 0 probability for all classes with observation 467Numerical 0 probability for all classes with observation 468Numerical 0 probability for all classes with observation 469Numerical 0 probability for all classes with observation 470Numerical 0 probability for all classes with observation 471Numerical 0 probability for all classes with observation 472Numerical 0 probability for all classes with observation 473Numerical 0 probability for all classes with observation 474Numerical 0 probability for all classes with observation 475Numerical 0 probability for all classes with observation 476Numerical 0 probability for all classes with observation 477Numerical 0 probability for all classes with observation 478Numerical 0 probability for all classes with observation 479Numerical 0 probability for all classes with observation 480Numerical 0 probability for all classes with observation 481Numerical 0 probability for all classes with observation 482Numerical 0 probability for all classes with observation 483Numerical 0 probability for all classes with observation 484Numerical 0 probability for all classes with observation 485Numerical 0 probability for all classes with observation 486Numerical 0 probability for all classes with observation 487Numerical 0 probability for all classes with observation 488Numerical 0 probability for all classes with observation 489Numerical 0 probability for all classes with observation 490Numerical 0 probability for all classes with observation 491Numerical 0 probability for all classes with observation 492Numerical 0 probability for all classes with observation 493Numerical 0 probability for all classes with observation 494Numerical 0 probability for all classes with observation 495Numerical 0 probability for all classes with observation 496Numerical 0 probability for all classes with observation 497Numerical 0 probability for all classes with observation 498Numerical 0 probability for all classes with observation 499Numerical 0 probability for all classes with observation 500Numerical 0 probability for all classes with observation 501Numerical 0 probability for all classes with observation 502Numerical 0 probability for all classes with observation 503Numerical 0 probability for all classes with observation 504Numerical 0 probability for all classes with observation 505Numerical 0 probability for all classes with observation 506Numerical 0 probability for all classes with observation 507Numerical 0 probability for all classes with observation 508Numerical 0 probability for all classes with observation 509Numerical 0 probability for all classes with observation 510Numerical 0 probability for all classes with observation 511Numerical 0 probability for all classes with observation 512Numerical 0 probability for all classes with observation 513Numerical 0 probability for all classes with observation 514Numerical 0 probability for all classes with observation 515Numerical 0 probability for all classes with observation 516Numerical 0 probability for all classes with observation 517Numerical 0 probability for all classes with observation 518Numerical 0 probability for all classes with observation 519Numerical 0 probability for all classes with observation 520Numerical 0 probability for all classes with observation 521Numerical 0 probability for all classes with observation 522Numerical 0 probability for all classes with observation 523Numerical 0 probability for all classes with observation 524Numerical 0 probability for all classes with observation 525Numerical 0 probability for all classes with observation 526Numerical 0 probability for all classes with observation 527Numerical 0 probability for all classes with observation 528Numerical 0 probability for all classes with observation 529Numerical 0 probability for all classes with observation 530Numerical 0 probability for all classes with observation 531Numerical 0 probability for all classes with observation 532Numerical 0 probability for all classes with observation 533Numerical 0 probability for all classes with observation 534Numerical 0 probability for all classes with observation 535Numerical 0 probability for all classes with observation 536Numerical 0 probability for all classes with observation 537Numerical 0 probability for all classes with observation 538Numerical 0 probability for all classes with observation 539Numerical 0 probability for all classes with observation 540Numerical 0 probability for all classes with observation 541Numerical 0 probability for all classes with observation 542Numerical 0 probability for all classes with observation 543Numerical 0 probability for all classes with observation 544Numerical 0 probability for all classes with observation 545Numerical 0 probability for all classes with observation 546Numerical 0 probability for all classes with observation 547Numerical 0 probability for all classes with observation 548Numerical 0 probability for all classes with observation 549Numerical 0 probability for all classes with observation 550Numerical 0 probability for all classes with observation 551Numerical 0 probability for all classes with observation 552Numerical 0 probability for all classes with observation 553Numerical 0 probability for all classes with observation 554Numerical 0 probability for all classes with observation 555Numerical 0 probability for all classes with observation 556Numerical 0 probability for all classes with observation 557Numerical 0 probability for all classes with observation 558Numerical 0 probability for all classes with observation 559Numerical 0 probability for all classes with observation 560Numerical 0 probability for all classes with observation 561Numerical 0 probability for all classes with observation 562Numerical 0 probability for all classes with observation 563Numerical 0 probability for all classes with observation 564Numerical 0 probability for all classes with observation 565Numerical 0 probability for all classes with observation 566Numerical 0 probability for all classes with observation 567Numerical 0 probability for all classes with observation 568Numerical 0 probability for all classes with observation 569Numerical 0 probability for all classes with observation 570Numerical 0 probability for all classes with observation 571Numerical 0 probability for all classes with observation 572Numerical 0 probability for all classes with observation 573Numerical 0 probability for all classes with observation 574Numerical 0 probability for all classes with observation 575Numerical 0 probability for all classes with observation 576Numerical 0 probability for all classes with observation 577Numerical 0 probability for all classes with observation 578Numerical 0 probability for all classes with observation 579Numerical 0 probability for all classes with observation 580Numerical 0 probability for all classes with observation 581Numerical 0 probability for all classes with observation 582Numerical 0 probability for all classes with observation 583Numerical 0 probability for all classes with observation 584Numerical 0 probability for all classes with observation 585Numerical 0 probability for all classes with observation 586Numerical 0 probability for all classes with observation 587Numerical 0 probability for all classes with observation 588Numerical 0 probability for all classes with observation 589Numerical 0 probability for all classes with observation 590Numerical 0 probability for all classes with observation 591Numerical 0 probability for all classes with observation 592Numerical 0 probability for all classes with observation 593Numerical 0 probability for all classes with observation 594Numerical 0 probability for all classes with observation 595Numerical 0 probability for all classes with observation 596Numerical 0 probability for all classes with observation 597Numerical 0 probability for all classes with observation 598Numerical 0 probability for all classes with observation 599Numerical 0 probability for all classes with observation 600Numerical 0 probability for all classes with observation 601Numerical 0 probability for all classes with observation 602Numerical 0 probability for all classes with observation 603Numerical 0 probability for all classes with observation 604Numerical 0 probability for all classes with observation 605Numerical 0 probability for all classes with observation 606Numerical 0 probability for all classes with observation 607Numerical 0 probability for all classes with observation 608Numerical 0 probability for all classes with observation 609Numerical 0 probability for all classes with observation 610Numerical 0 probability for all classes with observation 611Numerical 0 probability for all classes with observation 612Numerical 0 probability for all classes with observation 613Numerical 0 probability for all classes with observation 614Numerical 0 probability for all classes with observation 615Numerical 0 probability for all classes with observation 616Numerical 0 probability for all classes with observation 617Numerical 0 probability for all classes with observation 618Numerical 0 probability for all classes with observation 619Numerical 0 probability for all classes with observation 620Numerical 0 probability for all classes with observation 621Numerical 0 probability for all classes with observation 622Numerical 0 probability for all classes with observation 623Numerical 0 probability for all classes with observation 624Numerical 0 probability for all classes with observation 625Numerical 0 probability for all classes with observation 626Numerical 0 probability for all classes with observation 627Numerical 0 probability for all classes with observation 628Numerical 0 probability for all classes with observation 629Numerical 0 probability for all classes with observation 630Numerical 0 probability for all classes with observation 631Numerical 0 probability for all classes with observation 632Numerical 0 probability for all classes with observation 633Numerical 0 probability for all classes with observation 634Numerical 0 probability for all classes with observation 635Numerical 0 probability for all classes with observation 636Numerical 0 probability for all classes with observation 637Numerical 0 probability for all classes with observation 638Numerical 0 probability for all classes with observation 639Numerical 0 probability for all classes with observation 640Numerical 0 probability for all classes with observation 641Numerical 0 probability for all classes with observation 642Numerical 0 probability for all classes with observation 643Numerical 0 probability for all classes with observation 644Numerical 0 probability for all classes with observation 645Numerical 0 probability for all classes with observation 646Numerical 0 probability for all classes with observation 647Numerical 0 probability for all classes with observation 648Numerical 0 probability for all classes with observation 649Numerical 0 probability for all classes with observation 650Numerical 0 probability for all classes with observation 651Numerical 0 probability for all classes with observation 652Numerical 0 probability for all classes with observation 653Numerical 0 probability for all classes with observation 654Numerical 0 probability for all classes with observation 655Numerical 0 probability for all classes with observation 656Numerical 0 probability for all classes with observation 657Numerical 0 probability for all classes with observation 658Numerical 0 probability for all classes with observation 659Numerical 0 probability for all classes with observation 660Numerical 0 probability for all classes with observation 661Numerical 0 probability for all classes with observation 662Numerical 0 probability for all classes with observation 663Numerical 0 probability for all classes with observation 664Numerical 0 probability for all classes with observation 665Numerical 0 probability for all classes with observation 666Numerical 0 probability for all classes with observation 667Numerical 0 probability for all classes with observation 668Numerical 0 probability for all classes with observation 669Numerical 0 probability for all classes with observation 670Numerical 0 probability for all classes with observation 671Numerical 0 probability for all classes with observation 672Numerical 0 probability for all classes with observation 673Numerical 0 probability for all classes with observation 674Numerical 0 probability for all classes with observation 675Numerical 0 probability for all classes with observation 676Numerical 0 probability for all classes with observation 677Numerical 0 probability for all classes with observation 678Numerical 0 probability for all classes with observation 679Numerical 0 probability for all classes with observation 680Numerical 0 probability for all classes with observation 681Numerical 0 probability for all classes with observation 682Numerical 0 probability for all classes with observation 683Numerical 0 probability for all classes with observation 684Numerical 0 probability for all classes with observation 685Numerical 0 probability for all classes with observation 686Numerical 0 probability for all classes with observation 687Numerical 0 probability for all classes with observation 688Numerical 0 probability for all classes with observation 689Numerical 0 probability for all classes with observation 690Numerical 0 probability for all classes with observation 691Numerical 0 probability for all classes with observation 692Numerical 0 probability for all classes with observation 693Numerical 0 probability for all classes with observation 694Numerical 0 probability for all classes with observation 695Numerical 0 probability for all classes with observation 696Numerical 0 probability for all classes with observation 697Numerical 0 probability for all classes with observation 698Numerical 0 probability for all classes with observation 699Numerical 0 probability for all classes with observation 700Numerical 0 probability for all classes with observation 701Numerical 0 probability for all classes with observation 702Numerical 0 probability for all classes with observation 703Numerical 0 probability for all classes with observation 704Numerical 0 probability for all classes with observation 705Numerical 0 probability for all classes with observation 706Numerical 0 probability for all classes with observation 707Numerical 0 probability for all classes with observation 708Numerical 0 probability for all classes with observation 709Numerical 0 probability for all classes with observation 710Numerical 0 probability for all classes with observation 711Numerical 0 probability for all classes with observation 712Numerical 0 probability for all classes with observation 713Numerical 0 probability for all classes with observation 714Numerical 0 probability for all classes with observation 715Numerical 0 probability for all classes with observation 716Numerical 0 probability for all classes with observation 717Numerical 0 probability for all classes with observation 718Numerical 0 probability for all classes with observation 719Numerical 0 probability for all classes with observation 720Numerical 0 probability for all classes with observation 721Numerical 0 probability for all classes with observation 722Numerical 0 probability for all classes with observation 723Numerical 0 probability for all classes with observation 724Numerical 0 probability for all classes with observation 725Numerical 0 probability for all classes with observation 726Numerical 0 probability for all classes with observation 727Numerical 0 probability for all classes with observation 728Numerical 0 probability for all classes with observation 729Numerical 0 probability for all classes with observation 730Numerical 0 probability for all classes with observation 731Numerical 0 probability for all classes with observation 732Numerical 0 probability for all classes with observation 733Numerical 0 probability for all classes with observation 734Numerical 0 probability for all classes with observation 735Numerical 0 probability for all classes with observation 736Numerical 0 probability for all classes with observation 737Numerical 0 probability for all classes with observation 738Numerical 0 probability for all classes with observation 739Numerical 0 probability for all classes with observation 740Numerical 0 probability for all classes with observation 741Numerical 0 probability for all classes with observation 742Numerical 0 probability for all classes with observation 743Numerical 0 probability for all classes with observation 744Numerical 0 probability for all classes with observation 745Numerical 0 probability for all classes with observation 746Numerical 0 probability for all classes with observation 747Numerical 0 probability for all classes with observation 748Numerical 0 probability for all classes with observation 749Numerical 0 probability for all classes with observation 750Numerical 0 probability for all classes with observation 751Numerical 0 probability for all classes with observation 752Numerical 0 probability for all classes with observation 753Numerical 0 probability for all classes with observation 754Numerical 0 probability for all classes with observation 755Numerical 0 probability for all classes with observation 756Numerical 0 probability for all classes with observation 757Numerical 0 probability for all classes with observation 758Numerical 0 probability for all classes with observation 759Numerical 0 probability for all classes with observation 760Numerical 0 probability for all classes with observation 761Numerical 0 probability for all classes with observation 762Numerical 0 probability for all classes with observation 763Numerical 0 probability for all classes with observation 764Numerical 0 probability for all classes with observation 765Numerical 0 probability for all classes with observation 766Numerical 0 probability for all classes with observation 767Numerical 0 probability for all classes with observation 768Numerical 0 probability for all classes with observation 769Numerical 0 probability for all classes with observation 770Numerical 0 probability for all classes with observation 771Numerical 0 probability for all classes with observation 772Numerical 0 probability for all classes with observation 773Numerical 0 probability for all classes with observation 774Numerical 0 probability for all classes with observation 775Numerical 0 probability for all classes with observation 776Numerical 0 probability for all classes with observation 777Numerical 0 probability for all classes with observation 778Numerical 0 probability for all classes with observation 779Numerical 0 probability for all classes with observation 780Numerical 0 probability for all classes with observation 781Numerical 0 probability for all classes with observation 782Numerical 0 probability for all classes with observation 783Numerical 0 probability for all classes with observation 784Numerical 0 probability for all classes with observation 785Numerical 0 probability for all classes with observation 786Numerical 0 probability for all classes with observation 787Numerical 0 probability for all classes with observation 788Numerical 0 probability for all classes with observation 789Numerical 0 probability for all classes with observation 790Numerical 0 probability for all classes with observation 791Numerical 0 probability for all classes with observation 792Numerical 0 probability for all classes with observation 793Numerical 0 probability for all classes with observation 794Numerical 0 probability for all classes with observation 795Numerical 0 probability for all classes with observation 796Numerical 0 probability for all classes with observation 797Numerical 0 probability for all classes with observation 798Numerical 0 probability for all classes with observation 799Numerical 0 probability for all classes with observation 800Numerical 0 probability for all classes with observation 801Numerical 0 probability for all classes with observation 802Numerical 0 probability for all classes with observation 803Numerical 0 probability for all classes with observation 804Numerical 0 probability for all classes with observation 805Numerical 0 probability for all classes with observation 806Numerical 0 probability for all classes with observation 807Numerical 0 probability for all classes with observation 808Numerical 0 probability for all classes with observation 809Numerical 0 probability for all classes with observation 810Numerical 0 probability for all classes with observation 811Numerical 0 probability for all classes with observation 812Numerical 0 probability for all classes with observation 813Numerical 0 probability for all classes with observation 814Numerical 0 probability for all classes with observation 815Numerical 0 probability for all classes with observation 816Numerical 0 probability for all classes with observation 817Numerical 0 probability for all classes with observation 818Numerical 0 probability for all classes with observation 819Numerical 0 probability for all classes with observation 820Numerical 0 probability for all classes with observation 821Numerical 0 probability for all classes with observation 822Numerical 0 probability for all classes with observation 823Numerical 0 probability for all classes with observation 824Numerical 0 probability for all classes with observation 825Numerical 0 probability for all classes with observation 826Numerical 0 probability for all classes with observation 827Numerical 0 probability for all classes with observation 828Numerical 0 probability for all classes with observation 829Numerical 0 probability for all classes with observation 830Numerical 0 probability for all classes with observation 831Numerical 0 probability for all classes with observation 832Numerical 0 probability for all classes with observation 833Numerical 0 probability for all classes with observation 834model fit failed for Fold2.Rep1: usekernel=FALSE, fL=0, adjust=1 Error in NaiveBayes.default(x, y, usekernel = FALSE, fL = param$fL, ...) : 
  Zero variances for at least one class in variables: WAP001, WAP002, WAP009, WAP013, WAP014, WAP017, WAP018, WAP019, WAP020, WAP025, WAP026, WAP028, WAP039, WAP040, WAP041, WAP042, WAP047, WAP048, WAP049, WAP050, WAP051, WAP052, WAP055, WAP056, WAP057, WAP058, WAP071, WAP072, WAP080, WAP081, WAP086, WAP100, WAP133, WAP154, WAP157, WAP161, WAP162, WAP163, WAP193, WAP194, WAP195, WAP196, WAP198, WAP206, WAP207, WAP218, WAP219, WAP220, WAP228, WAP264, WAP265, WAP267, WAP269, WAP270, WAP271, WAP272, WAP273, WAP275, WAP276, WAP280, WAP281, WAP285, WAP287, WAP289, WAP290, WAP291, WAP292, WAP294, WAP299, WAP300, WAP302, WAP305, WAP306, WAP308, WAP309, WAP319, WAP320, WAP322, WAP324, WAP325, WAP326, WAP327, WAP328, WAP330, WAP331, WAP337, WAP341, WAP343, WAP345, WAP346, WAP347, WAP348, WAP350, WAP354, WAP355, WAP356, WAP359, WAP362, WAP363, WAP364, WAP376, WAP377, WAP379, WAP381, WAP382, WAP383, WAP384, WAP385, WAP387, WAP388, WAP393, WAP397, WAP399, WAP401, WAP402, WAP403, WAP409, WAP410, WAP411, WAP412, WAP413, WAP415, WAP417, WAP420, WAP421, WAP424, WAP426, WAP430, WAP434, WAP436, WAP437, WAP443, WAP447, WAP453, WAP454, WAP457, WAP459, WAP461, WAP462, WAP466, WAP467, WAP468, WAP476, WAP494, WAP500, WAP505, WAP509, WAP512, WAP515, WAP519
Numerical 0 probability for all classes with observation 1Numerical 0 probability for all classes with observation 2Numerical 0 probability for all classes with observation 3Numerical 0 probability for all classes with observation 4Numerical 0 probability for all classes with observation 5Numerical 0 probability for all classes with observation 6Numerical 0 probability for all classes with observation 7Numerical 0 probability for all classes with observation 8Numerical 0 probability for all classes with observation 9Numerical 0 probability for all classes with observation 10Numerical 0 probability for all classes with observation 11Numerical 0 probability for all classes with observation 12Numerical 0 probability for all classes with observation 13Numerical 0 probability for all classes with observation 14Numerical 0 probability for all classes with observation 15Numerical 0 probability for all classes with observation 16Numerical 0 probability for all classes with observation 17Numerical 0 probability for all classes with observation 18Numerical 0 probability for all classes with observation 19Numerical 0 probability for all classes with observation 20Numerical 0 probability for all classes with observation 21Numerical 0 probability for all classes with observation 22Numerical 0 probability for all classes with observation 23Numerical 0 probability for all classes with observation 24Numerical 0 probability for all classes with observation 25Numerical 0 probability for all classes with observation 26Numerical 0 probability for all classes with observation 27Numerical 0 probability for all classes with observation 28Numerical 0 probability for all classes with observation 29Numerical 0 probability for all classes with observation 30Numerical 0 probability for all classes with observation 31Numerical 0 probability for all classes with observation 32Numerical 0 probability for all classes with observation 33Numerical 0 probability for all classes with observation 34Numerical 0 probability for all classes with observation 35Numerical 0 probability for all classes with observation 36Numerical 0 probability for all classes with observation 37Numerical 0 probability for all classes with observation 38Numerical 0 probability for all classes with observation 39Numerical 0 probability for all classes with observation 40Numerical 0 probability for all classes with observation 41Numerical 0 probability for all classes with observation 42Numerical 0 probability for all classes with observation 43Numerical 0 probability for all classes with observation 44Numerical 0 probability for all classes with observation 45Numerical 0 probability for all classes with observation 46Numerical 0 probability for all classes with observation 47Numerical 0 probability for all classes with observation 48Numerical 0 probability for all classes with observation 49Numerical 0 probability for all classes with observation 50Numerical 0 probability for all classes with observation 51Numerical 0 probability for all classes with observation 52Numerical 0 probability for all classes with observation 53Numerical 0 probability for all classes with observation 54Numerical 0 probability for all classes with observation 55Numerical 0 probability for all classes with observation 56Numerical 0 probability for all classes with observation 57Numerical 0 probability for all classes with observation 58Numerical 0 probability for all classes with observation 59Numerical 0 probability for all classes with observation 60Numerical 0 probability for all classes with observation 61Numerical 0 probability for all classes with observation 62Numerical 0 probability for all classes with observation 63Numerical 0 probability for all classes with observation 64Numerical 0 probability for all classes with observation 65Numerical 0 probability for all classes with observation 66Numerical 0 probability for all classes with observation 67Numerical 0 probability for all classes with observation 68Numerical 0 probability for all classes with observation 69Numerical 0 probability for all classes with observation 70Numerical 0 probability for all classes with observation 71Numerical 0 probability for all classes with observation 72Numerical 0 probability for all classes with observation 73Numerical 0 probability for all classes with observation 74Numerical 0 probability for all classes with observation 75Numerical 0 probability for all classes with observation 76Numerical 0 probability for all classes with observation 77Numerical 0 probability for all classes with observation 78Numerical 0 probability for all classes with observation 79Numerical 0 probability for all classes with observation 80Numerical 0 probability for all classes with observation 81Numerical 0 probability for all classes with observation 82Numerical 0 probability for all classes with observation 83Numerical 0 probability for all classes with observation 84Numerical 0 probability for all classes with observation 85Numerical 0 probability for all classes with observation 86Numerical 0 probability for all classes with observation 87Numerical 0 probability for all classes with observation 88Numerical 0 probability for all classes with observation 89Numerical 0 probability for all classes with observation 90Numerical 0 probability for all classes with observation 91Numerical 0 probability for all classes with observation 92Numerical 0 probability for all classes with observation 93Numerical 0 probability for all classes with observation 94Numerical 0 probability for all classes with observation 95Numerical 0 probability for all classes with observation 96Numerical 0 probability for all classes with observation 97Numerical 0 probability for all classes with observation 98Numerical 0 probability for all classes with observation 99Numerical 0 probability for all classes with observation 100Numerical 0 probability for all classes with observation 101Numerical 0 probability for all classes with observation 102Numerical 0 probability for all classes with observation 103Numerical 0 probability for all classes with observation 104Numerical 0 probability for all classes with observation 105Numerical 0 probability for all classes with observation 106Numerical 0 probability for all classes with observation 107Numerical 0 probability for all classes with observation 108Numerical 0 probability for all classes with observation 109Numerical 0 probability for all classes with observation 110Numerical 0 probability for all classes with observation 111Numerical 0 probability for all classes with observation 112Numerical 0 probability for all classes with observation 113Numerical 0 probability for all classes with observation 114Numerical 0 probability for all classes with observation 115Numerical 0 probability for all classes with observation 116Numerical 0 probability for all classes with observation 117Numerical 0 probability for all classes with observation 118Numerical 0 probability for all classes with observation 119Numerical 0 probability for all classes with observation 120Numerical 0 probability for all classes with observation 121Numerical 0 probability for all classes with observation 122Numerical 0 probability for all classes with observation 123Numerical 0 probability for all classes with observation 124Numerical 0 probability for all classes with observation 125Numerical 0 probability for all classes with observation 126Numerical 0 probability for all classes with observation 127Numerical 0 probability for all classes with observation 128Numerical 0 probability for all classes with observation 129Numerical 0 probability for all classes with observation 130Numerical 0 probability for all classes with observation 131Numerical 0 probability for all classes with observation 132Numerical 0 probability for all classes with observation 133Numerical 0 probability for all classes with observation 134Numerical 0 probability for all classes with observation 135Numerical 0 probability for all classes with observation 136Numerical 0 probability for all classes with observation 137Numerical 0 probability for all classes with observation 138Numerical 0 probability for all classes with observation 139Numerical 0 probability for all classes with observation 140Numerical 0 probability for all classes with observation 141Numerical 0 probability for all classes with observation 142Numerical 0 probability for all classes with observation 143Numerical 0 probability for all classes with observation 144Numerical 0 probability for all classes with observation 145Numerical 0 probability for all classes with observation 146Numerical 0 probability for all classes with observation 147Numerical 0 probability for all classes with observation 148Numerical 0 probability for all classes with observation 149Numerical 0 probability for all classes with observation 150Numerical 0 probability for all classes with observation 151Numerical 0 probability for all classes with observation 152Numerical 0 probability for all classes with observation 153Numerical 0 probability for all classes with observation 154Numerical 0 probability for all classes with observation 155Numerical 0 probability for all classes with observation 156Numerical 0 probability for all classes with observation 157Numerical 0 probability for all classes with observation 158Numerical 0 probability for all classes with observation 159Numerical 0 probability for all classes with observation 160Numerical 0 probability for all classes with observation 161Numerical 0 probability for all classes with observation 162Numerical 0 probability for all classes with observation 163Numerical 0 probability for all classes with observation 164Numerical 0 probability for all classes with observation 165Numerical 0 probability for all classes with observation 166Numerical 0 probability for all classes with observation 167Numerical 0 probability for all classes with observation 168Numerical 0 probability for all classes with observation 169Numerical 0 probability for all classes with observation 170Numerical 0 probability for all classes with observation 171Numerical 0 probability for all classes with observation 172Numerical 0 probability for all classes with observation 173Numerical 0 probability for all classes with observation 174Numerical 0 probability for all classes with observation 175Numerical 0 probability for all classes with observation 176Numerical 0 probability for all classes with observation 177Numerical 0 probability for all classes with observation 178Numerical 0 probability for all classes with observation 179Numerical 0 probability for all classes with observation 180Numerical 0 probability for all classes with observation 181Numerical 0 probability for all classes with observation 182Numerical 0 probability for all classes with observation 183Numerical 0 probability for all classes with observation 184Numerical 0 probability for all classes with observation 185Numerical 0 probability for all classes with observation 186Numerical 0 probability for all classes with observation 187Numerical 0 probability for all classes with observation 188Numerical 0 probability for all classes with observation 189Numerical 0 probability for all classes with observation 190Numerical 0 probability for all classes with observation 191Numerical 0 probability for all classes with observation 192Numerical 0 probability for all classes with observation 193Numerical 0 probability for all classes with observation 194Numerical 0 probability for all classes with observation 195Numerical 0 probability for all classes with observation 196Numerical 0 probability for all classes with observation 197Numerical 0 probability for all classes with observation 198Numerical 0 probability for all classes with observation 199Numerical 0 probability for all classes with observation 200Numerical 0 probability for all classes with observation 201Numerical 0 probability for all classes with observation 202Numerical 0 probability for all classes with observation 203Numerical 0 probability for all classes with observation 204Numerical 0 probability for all classes with observation 205Numerical 0 probability for all classes with observation 206Numerical 0 probability for all classes with observation 207Numerical 0 probability for all classes with observation 208Numerical 0 probability for all classes with observation 209Numerical 0 probability for all classes with observation 210Numerical 0 probability for all classes with observation 211Numerical 0 probability for all classes with observation 212Numerical 0 probability for all classes with observation 213Numerical 0 probability for all classes with observation 214Numerical 0 probability for all classes with observation 215Numerical 0 probability for all classes with observation 216Numerical 0 probability for all classes with observation 217Numerical 0 probability for all classes with observation 218Numerical 0 probability for all classes with observation 219Numerical 0 probability for all classes with observation 220Numerical 0 probability for all classes with observation 221Numerical 0 probability for all classes with observation 222Numerical 0 probability for all classes with observation 223Numerical 0 probability for all classes with observation 224Numerical 0 probability for all classes with observation 225Numerical 0 probability for all classes with observation 226Numerical 0 probability for all classes with observation 227Numerical 0 probability for all classes with observation 228Numerical 0 probability for all classes with observation 229Numerical 0 probability for all classes with observation 230Numerical 0 probability for all classes with observation 231Numerical 0 probability for all classes with observation 232Numerical 0 probability for all classes with observation 233Numerical 0 probability for all classes with observation 234Numerical 0 probability for all classes with observation 235Numerical 0 probability for all classes with observation 236Numerical 0 probability for all classes with observation 237Numerical 0 probability for all classes with observation 238Numerical 0 probability for all classes with observation 239Numerical 0 probability for all classes with observation 240Numerical 0 probability for all classes with observation 241Numerical 0 probability for all classes with observation 242Numerical 0 probability for all classes with observation 243Numerical 0 probability for all classes with observation 244Numerical 0 probability for all classes with observation 245Numerical 0 probability for all classes with observation 246Numerical 0 probability for all classes with observation 247Numerical 0 probability for all classes with observation 248Numerical 0 probability for all classes with observation 249Numerical 0 probability for all classes with observation 250Numerical 0 probability for all classes with observation 251Numerical 0 probability for all classes with observation 252Numerical 0 probability for all classes with observation 253Numerical 0 probability for all classes with observation 254Numerical 0 probability for all classes with observation 255Numerical 0 probability for all classes with observation 256Numerical 0 probability for all classes with observation 257Numerical 0 probability for all classes with observation 258Numerical 0 probability for all classes with observation 259Numerical 0 probability for all classes with observation 260Numerical 0 probability for all classes with observation 261Numerical 0 probability for all classes with observation 262Numerical 0 probability for all classes with observation 263Numerical 0 probability for all classes with observation 264Numerical 0 probability for all classes with observation 265Numerical 0 probability for all classes with observation 266Numerical 0 probability for all classes with observation 267Numerical 0 probability for all classes with observation 268Numerical 0 probability for all classes with observation 269Numerical 0 probability for all classes with observation 270Numerical 0 probability for all classes with observation 271Numerical 0 probability for all classes with observation 272Numerical 0 probability for all classes with observation 273Numerical 0 probability for all classes with observation 274Numerical 0 probability for all classes with observation 275Numerical 0 probability for all classes with observation 276Numerical 0 probability for all classes with observation 277Numerical 0 probability for all classes with observation 278Numerical 0 probability for all classes with observation 279Numerical 0 probability for all classes with observation 280Numerical 0 probability for all classes with observation 281Numerical 0 probability for all classes with observation 282Numerical 0 probability for all classes with observation 283Numerical 0 probability for all classes with observation 284Numerical 0 probability for all classes with observation 285Numerical 0 probability for all classes with observation 286Numerical 0 probability for all classes with observation 287Numerical 0 probability for all classes with observation 288Numerical 0 probability for all classes with observation 289Numerical 0 probability for all classes with observation 290Numerical 0 probability for all classes with observation 291Numerical 0 probability for all classes with observation 292Numerical 0 probability for all classes with observation 293Numerical 0 probability for all classes with observation 294Numerical 0 probability for all classes with observation 295Numerical 0 probability for all classes with observation 296Numerical 0 probability for all classes with observation 297Numerical 0 probability for all classes with observation 298Numerical 0 probability for all classes with observation 299Numerical 0 probability for all classes with observation 300Numerical 0 probability for all classes with observation 301Numerical 0 probability for all classes with observation 302Numerical 0 probability for all classes with observation 303Numerical 0 probability for all classes with observation 304Numerical 0 probability for all classes with observation 305Numerical 0 probability for all classes with observation 306Numerical 0 probability for all classes with observation 307Numerical 0 probability for all classes with observation 308Numerical 0 probability for all classes with observation 309Numerical 0 probability for all classes with observation 310Numerical 0 probability for all classes with observation 311Numerical 0 probability for all classes with observation 312Numerical 0 probability for all classes with observation 313Numerical 0 probability for all classes with observation 314Numerical 0 probability for all classes with observation 315Numerical 0 probability for all classes with observation 316Numerical 0 probability for all classes with observation 317Numerical 0 probability for all classes with observation 318Numerical 0 probability for all classes with observation 319Numerical 0 probability for all classes with observation 320Numerical 0 probability for all classes with observation 321Numerical 0 probability for all classes with observation 322Numerical 0 probability for all classes with observation 323Numerical 0 probability for all classes with observation 324Numerical 0 probability for all classes with observation 325Numerical 0 probability for all classes with observation 326Numerical 0 probability for all classes with observation 327Numerical 0 probability for all classes with observation 328Numerical 0 probability for all classes with observation 329Numerical 0 probability for all classes with observation 330Numerical 0 probability for all classes with observation 331Numerical 0 probability for all classes with observation 332Numerical 0 probability for all classes with observation 333Numerical 0 probability for all classes with observation 334Numerical 0 probability for all classes with observation 335Numerical 0 probability for all classes with observation 336Numerical 0 probability for all classes with observation 337Numerical 0 probability for all classes with observation 338Numerical 0 probability for all classes with observation 339Numerical 0 probability for all classes with observation 340Numerical 0 probability for all classes with observation 341Numerical 0 probability for all classes with observation 342Numerical 0 probability for all classes with observation 343Numerical 0 probability for all classes with observation 344Numerical 0 probability for all classes with observation 345Numerical 0 probability for all classes with observation 346Numerical 0 probability for all classes with observation 347Numerical 0 probability for all classes with observation 348Numerical 0 probability for all classes with observation 349Numerical 0 probability for all classes with observation 350Numerical 0 probability for all classes with observation 351Numerical 0 probability for all classes with observation 352Numerical 0 probability for all classes with observation 353Numerical 0 probability for all classes with observation 354Numerical 0 probability for all classes with observation 355Numerical 0 probability for all classes with observation 356Numerical 0 probability for all classes with observation 357Numerical 0 probability for all classes with observation 358Numerical 0 probability for all classes with observation 359Numerical 0 probability for all classes with observation 360Numerical 0 probability for all classes with observation 361Numerical 0 probability for all classes with observation 362Numerical 0 probability for all classes with observation 363Numerical 0 probability for all classes with observation 364Numerical 0 probability for all classes with observation 365Numerical 0 probability for all classes with observation 366Numerical 0 probability for all classes with observation 367Numerical 0 probability for all classes with observation 368Numerical 0 probability for all classes with observation 369Numerical 0 probability for all classes with observation 370Numerical 0 probability for all classes with observation 371Numerical 0 probability for all classes with observation 372Numerical 0 probability for all classes with observation 373Numerical 0 probability for all classes with observation 374Numerical 0 probability for all classes with observation 375Numerical 0 probability for all classes with observation 376Numerical 0 probability for all classes with observation 377Numerical 0 probability for all classes with observation 378Numerical 0 probability for all classes with observation 379Numerical 0 probability for all classes with observation 380Numerical 0 probability for all classes with observation 381Numerical 0 probability for all classes with observation 382Numerical 0 probability for all classes with observation 383Numerical 0 probability for all classes with observation 384Numerical 0 probability for all classes with observation 385Numerical 0 probability for all classes with observation 386Numerical 0 probability for all classes with observation 387Numerical 0 probability for all classes with observation 388Numerical 0 probability for all classes with observation 389Numerical 0 probability for all classes with observation 390Numerical 0 probability for all classes with observation 391Numerical 0 probability for all classes with observation 392Numerical 0 probability for all classes with observation 393Numerical 0 probability for all classes with observation 394Numerical 0 probability for all classes with observation 395Numerical 0 probability for all classes with observation 396Numerical 0 probability for all classes with observation 397Numerical 0 probability for all classes with observation 398Numerical 0 probability for all classes with observation 399Numerical 0 probability for all classes with observation 400Numerical 0 probability for all classes with observation 401Numerical 0 probability for all classes with observation 402Numerical 0 probability for all classes with observation 403Numerical 0 probability for all classes with observation 404Numerical 0 probability for all classes with observation 405Numerical 0 probability for all classes with observation 406Numerical 0 probability for all classes with observation 407Numerical 0 probability for all classes with observation 408Numerical 0 probability for all classes with observation 409Numerical 0 probability for all classes with observation 410Numerical 0 probability for all classes with observation 411Numerical 0 probability for all classes with observation 412Numerical 0 probability for all classes with observation 413Numerical 0 probability for all classes with observation 414Numerical 0 probability for all classes with observation 415Numerical 0 probability for all classes with observation 416Numerical 0 probability for all classes with observation 417Numerical 0 probability for all classes with observation 418Numerical 0 probability for all classes with observation 419Numerical 0 probability for all classes with observation 420Numerical 0 probability for all classes with observation 421Numerical 0 probability for all classes with observation 422Numerical 0 probability for all classes with observation 423Numerical 0 probability for all classes with observation 424Numerical 0 probability for all classes with observation 425Numerical 0 probability for all classes with observation 426Numerical 0 probability for all classes with observation 427Numerical 0 probability for all classes with observation 428Numerical 0 probability for all classes with observation 429Numerical 0 probability for all classes with observation 430Numerical 0 probability for all classes with observation 431Numerical 0 probability for all classes with observation 432Numerical 0 probability for all classes with observation 433Numerical 0 probability for all classes with observation 434Numerical 0 probability for all classes with observation 435Numerical 0 probability for all classes with observation 436Numerical 0 probability for all classes with observation 437Numerical 0 probability for all classes with observation 438Numerical 0 probability for all classes with observation 439Numerical 0 probability for all classes with observation 440Numerical 0 probability for all classes with observation 441Numerical 0 probability for all classes with observation 442Numerical 0 probability for all classes with observation 443Numerical 0 probability for all classes with observation 444Numerical 0 probability for all classes with observation 445Numerical 0 probability for all classes with observation 446Numerical 0 probability for all classes with observation 447Numerical 0 probability for all classes with observation 448Numerical 0 probability for all classes with observation 449Numerical 0 probability for all classes with observation 450Numerical 0 probability for all classes with observation 451Numerical 0 probability for all classes with observation 452Numerical 0 probability for all classes with observation 453Numerical 0 probability for all classes with observation 454Numerical 0 probability for all classes with observation 455Numerical 0 probability for all classes with observation 456Numerical 0 probability for all classes with observation 457Numerical 0 probability for all classes with observation 458Numerical 0 probability for all classes with observation 459Numerical 0 probability for all classes with observation 460Numerical 0 probability for all classes with observation 461Numerical 0 probability for all classes with observation 462Numerical 0 probability for all classes with observation 463Numerical 0 probability for all classes with observation 464Numerical 0 probability for all classes with observation 465Numerical 0 probability for all classes with observation 466Numerical 0 probability for all classes with observation 467Numerical 0 probability for all classes with observation 468Numerical 0 probability for all classes with observation 469Numerical 0 probability for all classes with observation 470Numerical 0 probability for all classes with observation 471Numerical 0 probability for all classes with observation 472Numerical 0 probability for all classes with observation 473Numerical 0 probability for all classes with observation 474Numerical 0 probability for all classes with observation 475Numerical 0 probability for all classes with observation 476Numerical 0 probability for all classes with observation 477Numerical 0 probability for all classes with observation 478Numerical 0 probability for all classes with observation 479Numerical 0 probability for all classes with observation 480Numerical 0 probability for all classes with observation 481Numerical 0 probability for all classes with observation 482Numerical 0 probability for all classes with observation 483Numerical 0 probability for all classes with observation 484Numerical 0 probability for all classes with observation 485Numerical 0 probability for all classes with observation 486Numerical 0 probability for all classes with observation 487Numerical 0 probability for all classes with observation 488Numerical 0 probability for all classes with observation 489Numerical 0 probability for all classes with observation 490Numerical 0 probability for all classes with observation 491Numerical 0 probability for all classes with observation 492Numerical 0 probability for all classes with observation 493Numerical 0 probability for all classes with observation 494Numerical 0 probability for all classes with observation 495Numerical 0 probability for all classes with observation 496Numerical 0 probability for all classes with observation 497Numerical 0 probability for all classes with observation 498Numerical 0 probability for all classes with observation 499Numerical 0 probability for all classes with observation 500Numerical 0 probability for all classes with observation 501Numerical 0 probability for all classes with observation 502Numerical 0 probability for all classes with observation 503Numerical 0 probability for all classes with observation 504Numerical 0 probability for all classes with observation 505Numerical 0 probability for all classes with observation 506Numerical 0 probability for all classes with observation 507Numerical 0 probability for all classes with observation 508Numerical 0 probability for all classes with observation 509Numerical 0 probability for all classes with observation 510Numerical 0 probability for all classes with observation 511Numerical 0 probability for all classes with observation 512Numerical 0 probability for all classes with observation 513Numerical 0 probability for all classes with observation 514Numerical 0 probability for all classes with observation 515Numerical 0 probability for all classes with observation 516Numerical 0 probability for all classes with observation 517Numerical 0 probability for all classes with observation 518Numerical 0 probability for all classes with observation 519Numerical 0 probability for all classes with observation 520Numerical 0 probability for all classes with observation 521Numerical 0 probability for all classes with observation 522Numerical 0 probability for all classes with observation 523Numerical 0 probability for all classes with observation 524Numerical 0 probability for all classes with observation 525Numerical 0 probability for all classes with observation 526Numerical 0 probability for all classes with observation 527Numerical 0 probability for all classes with observation 528Numerical 0 probability for all classes with observation 529Numerical 0 probability for all classes with observation 530Numerical 0 probability for all classes with observation 531Numerical 0 probability for all classes with observation 532Numerical 0 probability for all classes with observation 533Numerical 0 probability for all classes with observation 534Numerical 0 probability for all classes with observation 535Numerical 0 probability for all classes with observation 536Numerical 0 probability for all classes with observation 537Numerical 0 probability for all classes with observation 538Numerical 0 probability for all classes with observation 539Numerical 0 probability for all classes with observation 540Numerical 0 probability for all classes with observation 541Numerical 0 probability for all classes with observation 542Numerical 0 probability for all classes with observation 543Numerical 0 probability for all classes with observation 544Numerical 0 probability for all classes with observation 545Numerical 0 probability for all classes with observation 546Numerical 0 probability for all classes with observation 547Numerical 0 probability for all classes with observation 548Numerical 0 probability for all classes with observation 549Numerical 0 probability for all classes with observation 550Numerical 0 probability for all classes with observation 551Numerical 0 probability for all classes with observation 552Numerical 0 probability for all classes with observation 553Numerical 0 probability for all classes with observation 554Numerical 0 probability for all classes with observation 555Numerical 0 probability for all classes with observation 556Numerical 0 probability for all classes with observation 557Numerical 0 probability for all classes with observation 558Numerical 0 probability for all classes with observation 559Numerical 0 probability for all classes with observation 560Numerical 0 probability for all classes with observation 561Numerical 0 probability for all classes with observation 562Numerical 0 probability for all classes with observation 563Numerical 0 probability for all classes with observation 564Numerical 0 probability for all classes with observation 565Numerical 0 probability for all classes with observation 566Numerical 0 probability for all classes with observation 567Numerical 0 probability for all classes with observation 568Numerical 0 probability for all classes with observation 569Numerical 0 probability for all classes with observation 570Numerical 0 probability for all classes with observation 571Numerical 0 probability for all classes with observation 572Numerical 0 probability for all classes with observation 573Numerical 0 probability for all classes with observation 574Numerical 0 probability for all classes with observation 575Numerical 0 probability for all classes with observation 576Numerical 0 probability for all classes with observation 577Numerical 0 probability for all classes with observation 578Numerical 0 probability for all classes with observation 579Numerical 0 probability for all classes with observation 580Numerical 0 probability for all classes with observation 581Numerical 0 probability for all classes with observation 582Numerical 0 probability for all classes with observation 583Numerical 0 probability for all classes with observation 584Numerical 0 probability for all classes with observation 585Numerical 0 probability for all classes with observation 586Numerical 0 probability for all classes with observation 587Numerical 0 probability for all classes with observation 588Numerical 0 probability for all classes with observation 589Numerical 0 probability for all classes with observation 590Numerical 0 probability for all classes with observation 591Numerical 0 probability for all classes with observation 592Numerical 0 probability for all classes with observation 593Numerical 0 probability for all classes with observation 594Numerical 0 probability for all classes with observation 595Numerical 0 probability for all classes with observation 596Numerical 0 probability for all classes with observation 597Numerical 0 probability for all classes with observation 598Numerical 0 probability for all classes with observation 599Numerical 0 probability for all classes with observation 600Numerical 0 probability for all classes with observation 601Numerical 0 probability for all classes with observation 602Numerical 0 probability for all classes with observation 603Numerical 0 probability for all classes with observation 604Numerical 0 probability for all classes with observation 605Numerical 0 probability for all classes with observation 606Numerical 0 probability for all classes with observation 607Numerical 0 probability for all classes with observation 608Numerical 0 probability for all classes with observation 609Numerical 0 probability for all classes with observation 610Numerical 0 probability for all classes with observation 611Numerical 0 probability for all classes with observation 612Numerical 0 probability for all classes with observation 613Numerical 0 probability for all classes with observation 614Numerical 0 probability for all classes with observation 615Numerical 0 probability for all classes with observation 616Numerical 0 probability for all classes with observation 617Numerical 0 probability for all classes with observation 618Numerical 0 probability for all classes with observation 619Numerical 0 probability for all classes with observation 620Numerical 0 probability for all classes with observation 621Numerical 0 probability for all classes with observation 622Numerical 0 probability for all classes with observation 623Numerical 0 probability for all classes with observation 624Numerical 0 probability for all classes with observation 625Numerical 0 probability for all classes with observation 626Numerical 0 probability for all classes with observation 627Numerical 0 probability for all classes with observation 628Numerical 0 probability for all classes with observation 629Numerical 0 probability for all classes with observation 630Numerical 0 probability for all classes with observation 631Numerical 0 probability for all classes with observation 632Numerical 0 probability for all classes with observation 633Numerical 0 probability for all classes with observation 634Numerical 0 probability for all classes with observation 635Numerical 0 probability for all classes with observation 636Numerical 0 probability for all classes with observation 637Numerical 0 probability for all classes with observation 638Numerical 0 probability for all classes with observation 639Numerical 0 probability for all classes with observation 640Numerical 0 probability for all classes with observation 641Numerical 0 probability for all classes with observation 642Numerical 0 probability for all classes with observation 643Numerical 0 probability for all classes with observation 644Numerical 0 probability for all classes with observation 645Numerical 0 probability for all classes with observation 646Numerical 0 probability for all classes with observation 647Numerical 0 probability for all classes with observation 648Numerical 0 probability for all classes with observation 649Numerical 0 probability for all classes with observation 650Numerical 0 probability for all classes with observation 651Numerical 0 probability for all classes with observation 652Numerical 0 probability for all classes with observation 653Numerical 0 probability for all classes with observation 654Numerical 0 probability for all classes with observation 655Numerical 0 probability for all classes with observation 656Numerical 0 probability for all classes with observation 657Numerical 0 probability for all classes with observation 658Numerical 0 probability for all classes with observation 659Numerical 0 probability for all classes with observation 660Numerical 0 probability for all classes with observation 661Numerical 0 probability for all classes with observation 662Numerical 0 probability for all classes with observation 663Numerical 0 probability for all classes with observation 664Numerical 0 probability for all classes with observation 665Numerical 0 probability for all classes with observation 666Numerical 0 probability for all classes with observation 667Numerical 0 probability for all classes with observation 668Numerical 0 probability for all classes with observation 669Numerical 0 probability for all classes with observation 670Numerical 0 probability for all classes with observation 671Numerical 0 probability for all classes with observation 672Numerical 0 probability for all classes with observation 673Numerical 0 probability for all classes with observation 674Numerical 0 probability for all classes with observation 675Numerical 0 probability for all classes with observation 676Numerical 0 probability for all classes with observation 677Numerical 0 probability for all classes with observation 678Numerical 0 probability for all classes with observation 679Numerical 0 probability for all classes with observation 680Numerical 0 probability for all classes with observation 681Numerical 0 probability for all classes with observation 682Numerical 0 probability for all classes with observation 683Numerical 0 probability for all classes with observation 684Numerical 0 probability for all classes with observation 685Numerical 0 probability for all classes with observation 686Numerical 0 probability for all classes with observation 687Numerical 0 probability for all classes with observation 688Numerical 0 probability for all classes with observation 689Numerical 0 probability for all classes with observation 690Numerical 0 probability for all classes with observation 691Numerical 0 probability for all classes with observation 692Numerical 0 probability for all classes with observation 693Numerical 0 probability for all classes with observation 694Numerical 0 probability for all classes with observation 695Numerical 0 probability for all classes with observation 696Numerical 0 probability for all classes with observation 697Numerical 0 probability for all classes with observation 698Numerical 0 probability for all classes with observation 699Numerical 0 probability for all classes with observation 700Numerical 0 probability for all classes with observation 701Numerical 0 probability for all classes with observation 702Numerical 0 probability for all classes with observation 703Numerical 0 probability for all classes with observation 704Numerical 0 probability for all classes with observation 705Numerical 0 probability for all classes with observation 706Numerical 0 probability for all classes with observation 707Numerical 0 probability for all classes with observation 708Numerical 0 probability for all classes with observation 709Numerical 0 probability for all classes with observation 710Numerical 0 probability for all classes with observation 711Numerical 0 probability for all classes with observation 712Numerical 0 probability for all classes with observation 713Numerical 0 probability for all classes with observation 714Numerical 0 probability for all classes with observation 715Numerical 0 probability for all classes with observation 716Numerical 0 probability for all classes with observation 717Numerical 0 probability for all classes with observation 718Numerical 0 probability for all classes with observation 719Numerical 0 probability for all classes with observation 720Numerical 0 probability for all classes with observation 721Numerical 0 probability for all classes with observation 722Numerical 0 probability for all classes with observation 723Numerical 0 probability for all classes with observation 724Numerical 0 probability for all classes with observation 725Numerical 0 probability for all classes with observation 726Numerical 0 probability for all classes with observation 727Numerical 0 probability for all classes with observation 728Numerical 0 probability for all classes with observation 729Numerical 0 probability for all classes with observation 730Numerical 0 probability for all classes with observation 731Numerical 0 probability for all classes with observation 732Numerical 0 probability for all classes with observation 733Numerical 0 probability for all classes with observation 734Numerical 0 probability for all classes with observation 735Numerical 0 probability for all classes with observation 736Numerical 0 probability for all classes with observation 737Numerical 0 probability for all classes with observation 738Numerical 0 probability for all classes with observation 739Numerical 0 probability for all classes with observation 740Numerical 0 probability for all classes with observation 741Numerical 0 probability for all classes with observation 742Numerical 0 probability for all classes with observation 743Numerical 0 probability for all classes with observation 744Numerical 0 probability for all classes with observation 745Numerical 0 probability for all classes with observation 746Numerical 0 probability for all classes with observation 747Numerical 0 probability for all classes with observation 748Numerical 0 probability for all classes with observation 749Numerical 0 probability for all classes with observation 750Numerical 0 probability for all classes with observation 751Numerical 0 probability for all classes with observation 752Numerical 0 probability for all classes with observation 753Numerical 0 probability for all classes with observation 754Numerical 0 probability for all classes with observation 755Numerical 0 probability for all classes with observation 756Numerical 0 probability for all classes with observation 757Numerical 0 probability for all classes with observation 758Numerical 0 probability for all classes with observation 759Numerical 0 probability for all classes with observation 760Numerical 0 probability for all classes with observation 761Numerical 0 probability for all classes with observation 762Numerical 0 probability for all classes with observation 763Numerical 0 probability for all classes with observation 764Numerical 0 probability for all classes with observation 765Numerical 0 probability for all classes with observation 766Numerical 0 probability for all classes with observation 767Numerical 0 probability for all classes with observation 768Numerical 0 probability for all classes with observation 769Numerical 0 probability for all classes with observation 770Numerical 0 probability for all classes with observation 771Numerical 0 probability for all classes with observation 772Numerical 0 probability for all classes with observation 773Numerical 0 probability for all classes with observation 774Numerical 0 probability for all classes with observation 775Numerical 0 probability for all classes with observation 776Numerical 0 probability for all classes with observation 777Numerical 0 probability for all classes with observation 778Numerical 0 probability for all classes with observation 779Numerical 0 probability for all classes with observation 780Numerical 0 probability for all classes with observation 781Numerical 0 probability for all classes with observation 782Numerical 0 probability for all classes with observation 783Numerical 0 probability for all classes with observation 784Numerical 0 probability for all classes with observation 785Numerical 0 probability for all classes with observation 786Numerical 0 probability for all classes with observation 787Numerical 0 probability for all classes with observation 788Numerical 0 probability for all classes with observation 789Numerical 0 probability for all classes with observation 790Numerical 0 probability for all classes with observation 791Numerical 0 probability for all classes with observation 792Numerical 0 probability for all classes with observation 793Numerical 0 probability for all classes with observation 794Numerical 0 probability for all classes with observation 795Numerical 0 probability for all classes with observation 796Numerical 0 probability for all classes with observation 797Numerical 0 probability for all classes with observation 798Numerical 0 probability for all classes with observation 799Numerical 0 probability for all classes with observation 800Numerical 0 probability for all classes with observation 801Numerical 0 probability for all classes with observation 802Numerical 0 probability for all classes with observation 803Numerical 0 probability for all classes with observation 804Numerical 0 probability for all classes with observation 805Numerical 0 probability for all classes with observation 806Numerical 0 probability for all classes with observation 807Numerical 0 probability for all classes with observation 808Numerical 0 probability for all classes with observation 809Numerical 0 probability for all classes with observation 810Numerical 0 probability for all classes with observation 811Numerical 0 probability for all classes with observation 812Numerical 0 probability for all classes with observation 813Numerical 0 probability for all classes with observation 814Numerical 0 probability for all classes with observation 815Numerical 0 probability for all classes with observation 816Numerical 0 probability for all classes with observation 817Numerical 0 probability for all classes with observation 818Numerical 0 probability for all classes with observation 819Numerical 0 probability for all classes with observation 820Numerical 0 probability for all classes with observation 821Numerical 0 probability for all classes with observation 822Numerical 0 probability for all classes with observation 823Numerical 0 probability for all classes with observation 824Numerical 0 probability for all classes with observation 825Numerical 0 probability for all classes with observation 826Numerical 0 probability for all classes with observation 827Numerical 0 probability for all classes with observation 828Numerical 0 probability for all classes with observation 829Numerical 0 probability for all classes with observation 830Numerical 0 probability for all classes with observation 831Numerical 0 probability for all classes with observation 832model fit failed for Fold3.Rep1: usekernel=FALSE, fL=0, adjust=1 Error in NaiveBayes.default(x, y, usekernel = FALSE, fL = param$fL, ...) : 
  Zero variances for at least one class in variables: WAP001, WAP002, WAP009, WAP017, WAP018, WAP019, WAP020, WAP025, WAP026, WAP028, WAP047, WAP048, WAP049, WAP050, WAP051, WAP052, WAP055, WAP056, WAP057, WAP058, WAP071, WAP072, WAP080, WAP081, WAP086, WAP100, WAP133, WAP154, WAP157, WAP162, WAP163, WAP193, WAP194, WAP195, WAP196, WAP198, WAP199, WAP206, WAP207, WAP214, WAP218, WAP219, WAP220, WAP228, WAP264, WAP265, WAP267, WAP269, WAP270, WAP271, WAP272, WAP273, WAP275, WAP276, WAP280, WAP281, WAP285, WAP287, WAP290, WAP291, WAP292, WAP294, WAP299, WAP300, WAP302, WAP305, WAP306, WAP308, WAP309, WAP319, WAP320, WAP322, WAP324, WAP325, WAP326, WAP327, WAP328, WAP330, WAP331, WAP337, WAP341, WAP343, WAP345, WAP346, WAP347, WAP348, WAP350, WAP354, WAP355, WAP356, WAP359, WAP362, WAP363, WAP364, WAP376, WAP377, WAP379, WAP381, WAP382, WAP383, WAP384, WAP385, WAP387, WAP388, WAP393, WAP397, WAP399, WAP402, WAP403, WAP409, WAP410, WAP411, WAP412, WAP413, WAP415, WAP417, WAP420, WAP421, WAP424, WAP426, WAP430, WAP434, WAP436, WAP437, WAP443, WAP447, WAP454, WAP457, WAP459, WAP461, WAP462, WAP466, WAP467, WAP468, WAP476, WAP494, WAP500, WAP505, WAP506, WAP508, WAP509, WAP512, WAP515, WAP519
There were missing values in resampled performance measures.missing values found in aggregated results

nbfit_RP

Naive Bayes 

2500 samples
 408 predictor
   2 classes: '1', '2' 

No pre-processing
Resampling: Cross-Validated (3 fold, repeated 1 times) 
Summary of sample sizes: 1666, 1666, 1668 
Resampling results across tuning parameters:

  usekernel  Accuracy   Kappa
  FALSE            NaN  NaN  
   TRUE      0.8492004    0  

Tuning parameter 'fL' was held constant at a value of 0
Tuning parameter 'adjust' was held constant at a value of 1
Accuracy was used to select the optimal model using the largest value.
The final values used for the model were fL = 0, usekernel = TRUE and adjust = 1.

gbmfit_RP <- train(RELATIVEPOSITION~., #y/target
                 data = df_train_RP, #X/features
                 metric = 'Kappa', #Metric applied
                 method = "gbm", #ML algorithm
                 trControl=gbmfitControl, #Apply CV to the training
                 tuneLength = 2, # Number of levels for each tuning parameters that should be generated
                 verbose = FALSE)

variable 2: WAP002 has no variation.variable 181: WAP194 has no variation.variable 189: WAP207 has no variation.variable 253: WAP309 has no variation.variable 292: WAP354 has no variation.variable 345: WAP421 has no variation.variable 362: WAP454 has no variation.variable 369: WAP462 has no variation.variable 2: WAP002 has no variation.variable 181: WAP194 has no variation.variable 189: WAP207 has no variation.variable 253: WAP309 has no variation.variable 292: WAP354 has no variation.variable 345: WAP421 has no variation.variable 362: WAP454 has no variation.variable 369: WAP462 has no variation.variable 83: WAP086 has no variation.variable 184: WAP198 has no variation.variable 198: WAP228 has no variation.variable 228: WAP275 has no variation.variable 237: WAP285 has no variation.variable 273: WAP330 has no variation.variable 274: WAP331 has no variation.variable 288: WAP347 has no variation.variable 339: WAP412 has no variation.variable 342: WAP417 has no variation.variable 344: WAP420 has no variation.variable 373: WAP468 has no variation.variable 396: WAP505 has no variation.variable 401: WAP512 has no variation.variable 83: WAP086 has no variation.variable 184: WAP198 has no variation.variable 198: WAP228 has no variation.variable 228: WAP275 has no variation.variable 237: WAP285 has no variation.variable 273: WAP330 has no variation.variable 274: WAP331 has no variation.variable 288: WAP347 has no variation.variable 339: WAP412 has no variation.variable 342: WAP417 has no variation.variable 344: WAP420 has no variation.variable 373: WAP468 has no variation.variable 396: WAP505 has no variation.variable 401: WAP512 has no variation.variable 53: WAP055 has no variation.variable 54: WAP056 has no variation.variable 126: WAP133 has no variation.variable 182: WAP195 has no variation.variable 188: WAP206 has no variation.variable 193: WAP220 has no variation.variable 284: WAP343 has no variation.variable 318: WAP387 has no variation.variable 347: WAP424 has no variation.variable 350: WAP430 has no variation.variable 355: WAP437 has no variation.variable 365: WAP457 has no variation.variable 371: WAP466 has no variation.variable 399: WAP509 has no variation.variable 407: WAP518 has no variation.variable 408: WAP519 has no variation.variable 53: WAP055 has no variation.variable 54: WAP056 has no variation.variable 126: WAP133 has no variation.variable 182: WAP195 has no variation.variable 188: WAP206 has no variation.variable 193: WAP220 has no variation.variable 284: WAP343 has no variation.variable 318: WAP387 has no variation.variable 347: WAP424 has no variation.variable 350: WAP430 has no variation.variable 355: WAP437 has no variation.variable 365: WAP457 has no variation.variable 371: WAP466 has no variation.variable 399: WAP509 has no variation.variable 407: WAP518 has no variation.variable 408: WAP519 has no variation.

gbmfit_RP

Stochastic Gradient Boosting 

2500 samples
 408 predictor
   2 classes: '1', '2' 

No pre-processing
Resampling: Cross-Validated (3 fold, repeated 1 times) 
Summary of sample sizes: 1667, 1666, 1667 
Resampling results across tuning parameters:

  interaction.depth  n.trees  Accuracy   Kappa     
  1                   50      0.8480016  0.02282711
  1                  100      0.8456020  0.05502141
  2                   50      0.8440019  0.04517745
  2                  100      0.8448022  0.12689749

Tuning parameter 'shrinkage' was held constant at a value of 0.1
Tuning parameter 'n.minobsinnode' was held constant at a value of 10
Kappa was used to select the optimal model using the largest value.
The final values used for the model were n.trees = 100, interaction.depth = 2, shrinkage = 0.1 and n.minobsinnode = 10.

rffit_RP <- train(RELATIVEPOSITION~., #y/target
                 data = df_train_RP, #X/features
                 metric = 'Kappa', #Metric applied
                 method = "rf", #ML algorithm
                 trControl=rffitControl, #Apply CV to the training
                 tuneLength = 2, # Number of levels for each tuning parameters that should be generated
                 verbose = FALSE)

As asked, in this part we are supposed to train a model using Stochastic Gradient Boosting, GBM, on the training set with 10-fold cross-validation and an Automatic Tuning Grid, which is what is coded above.

Train function chooses the model with the largest performance value (or smallest, for mean squared error in regression models), therefore there is no need to select the best iteration of the models.

varImp(nbfit_RP)

varImp(gbmfit_RP)

varImp(rffit_RP)

As predicted the salary variable is the most relevant in predicting the target variable. Age comes in a close second place. The remaining variables have a really low relative impact when forecasting the target.

pred_GBM <- predict(gbmFit1, newdata = testing)

Prob_pred_GBM <- predict(gbmFit1, newdata = testing, type = "prob")

postResample(pred_GBM, testing$brand)

This model provides an accuracy of ~94% which is pretty high. The Kappa or Cohen’s Kappa is at ~86% which is quite impressive since this metric is normalized at the baseline of random chance on our dataset. This dataset has a slightly unbalanced target, therefore the Kappa value is quite different from the accuracy value. It’s worth adding that if the model was trained to optimise the accuracy, the metrics accuracy and Kappa obtained would be respectively: 0.932498 0.856289. Therefore optimising this model to the metric “Kappa” is a much better alternative for this dataset as it provided better results in both metrics!

confusionMatrix(data = pred_GBM, 
                reference = testing$brand, 
                positive = "1")

The confusion matrix is quite solid, the auxiliary statistical metrics derived, seem to confirm so. Below, I commented how each of the metrics calculated from the confusion matrix support that the model has a good performance overall: - Accuracy: This is the most intuitive performance measure and it is simply a ratio of correctly predicted observation to the total observations ((TN+TP)/Total). Forecasting correctly ~94% of the test observations is pretty good; - 95% CI: The 95% confidence interval estimates that the accuracy falls within an interval with low variation within a high performance. - No information rate: The “no-information rate” is the largest proportion of the observed classes. The test set contains 62% class 1 (Sony) and only (100-62)=38% class 0 (Acer); - P-Value: A p-value, or probability value, is a number describing how likely it is that your data would have occurred by random chance (i.e. that the null hypothesis is true). In this case the p-value is clearly smaller than the the reference of 0.05, meaning that the p-value is statistically significant and the null hypothesis may be rejected;

• Kappa: The Kappa has been explained and commented above;

• Mcnemar’s Test P-Value: In terms of comparing two binary classification algorithms, the test is commenting on whether the two models disagree in the same way (or not). It is not commenting on whether one model is more or less accurate or error prone than another. This is clear when we look at how the statistic is calculated. In this case we have fed a confusion matrix to the function and not a contingency table (comparing simply the number of correct vs. incorrect observations while discounting the classes);

• Sensitivity: Proportion of those who correctly received a positive result (class 1 - Sony) on this test out of those who actually have a positive result (TP/(TP+FN)). The value obtained for this metric is ~95% which is alright;

• Specificity: Proportion of those who correctly received a negative result (class 0 - Acer) on this test out of those who actually have a negative result (TN/(FP+TN)). The percentage of correctly predicted Sony is higher than Acer;

• Pos Pred Value: Proportion of positive results that are true positive (TP/(TP+FP));

• Neg Pred Value: Proportion of negative results that are true negative (TN/(TN+FN)). This model has a higher accuracy in forecasting class 1 (Sony) relatively to class 0;

• Prevalence: Measure of the frequency of a condition in a population at a particular point in time ((TP+FN)/Total). In this case the condition measured is the positives. As can be seen this dataset is slightly unbalanced;

• Detection Rate: Here the detection rate is defined as the fraction of observations who are in fact positive and are called positive by the model (TP/Total). Fortunately, this percentage is similar to the prevalence meaning that the model captured the class skewness of this dataset. If the value was too different the False Negatives would be hindering the model’s performance;

• Detection Prevalence: This is defined as the number of predicted positive events (both true positive and false positive) divided by the total number of predictions ((TP+FP)/Total). This value is similar to what was obtained in the prevalence metric, this indicates that the amount of false negatives is simillar to the false positives when considering the whole test dataset;

• Balanced Accuracy: Balanced accuracy attempts to account for the imbalance in classes ((TPR+TNR)/2 = (Sensitivity+Specificity)/2). The balanced accuracy is slightly lower than the accuracy. Nonetheless, this metric is at 92%, thus this model clearly captured the data unbalance and is not just supposing that the most frequent class is the correct one (in this case the balanced accuracy would be 50% and the accuracy would coincide with the proportion of the most frequent class relatively to the less occuring one).

temp_pred_GB = factor(ifelse(pred_GBM == 1, "Y", "N"))
temp_obs_GB = factor(ifelse(testing$brand == 1, "Y", "N"))

twoClassSummary(data = data.frame(obs = temp_obs_GB, pred = temp_pred_GB, Y = Prob_pred_GBM$'1', N = Prob_pred_GBM$'0'), lev = levels(temp_pred_GB))
#For some reason, this function does not seem to provide ROC results if a binary numerical labeling is used, I had to convert '1' into 'Y' and '0' into 'N' to obtain valid results

mnLogLoss(data = data.frame(obs = temp_obs_GB, pred = temp_pred_GB, Y = Prob_pred_GBM$'1', N = Prob_pred_GBM$'0'), lev = levels(temp_pred_GB))

The area under the ROC curve is close to 1 meaning that the classifier is far better than a random classifier (AUC of 0.5). In fact, the AUC is close to 1, a perfect classifier. The value of the specificity and specificity seem to have swapped among themselves (the values calculated in the function above are the correct ones), thus, I will not comment these values. - Log Loss: Log-loss is indicative of how close the prediction probability is to the corresponding actual/true value (0 or 1 in case of binary classification). The more the predicted probability diverges from the actual value, the higher is the log-loss value. In the case of the LogLoss metric, one usual “well-known” metric is to say that 0.693 is the non-informative value. This figure is obtained by predicting p = 0.5 for any class of a binary problem. This is valid only for balanced binary problems. Because we have obtained a Log Loss of 0.218, much lower than 0.693, we can afirm that this model is clearly better than random picking and has captured the problem.